
4)j>yZ 



DEPARTMENT OF THE INTERIOR 
UNITED STATES GEOLOGICAL SURVEY 

GEORGE OTIS SMITH, Director 



INSTRUCTIONS TO 
TOPOGRAPHERS 



OF THE 



UNITED' STATES GEOLOGICAL 
SURVEY 




WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1911 



% 



DEPARTMENT OF THE INTERIOR 

UNITED STATES GEOLOGICAL SURVEY 

GEORGE OTIS SMITH, Director 



INSTRUCTIONS TO 
TOPOGRAPHERS 



5 V? 



OF THE 



UNITED STATES GEOLOGICAL 
SURVEY* 




WASHINGTON 

GOVERNMENT PRINTING OFFICE 
1911 







s 



ft. 






CONTENTS. 

Page. 

Prefatory note 5 

Horizontal control ; 7 

General conditions 7 

Primary triangulation 

Field work 8 

Computations 21 

General suggestions to computers 37 

Primary traverse 39 

Field work 39 

Computations 47 

Vertical control 52 

Primary and precise leveling , . 52 

General instructions 52 

Primary leveling with Y level 56 

Primary leveling with yard rod and prism level 59 

Precise leveling 64 

Special instructions for use of prism level notebook 
9-940 when used for primary or precise leveling 

record 65 

Computation and adjustment of level circuits 70 

Adjustment of instruments t ; 75 

Telescopic alidade . 75 

Y level 76 

Locke level , 77 

Rod level , 78 

Transit 78 

Theodolite 80 

3 



PREFATORY NOTE. 

The following instructions will eventually be incorporated in a 
handbook of instructions which is in preparation for topographers 
of the Geological Survey. They are printed in the present form 
for temporary use, and any criticisms or suggestions that would 
tend to improve them should be sent promptly to the chief geog- 
rapher. 



Approved : 

Geo. Otis Smith, Director. 
Washington, D. C, June 30, ign, 



R. B. Marshall, 

Chief Geographer. 



U. S. GEOLOGICAL SURVEY 



INSTRUCTIONS TO TOPOGRAPHERS PLATE I 




7/feft 



7 



MARKS FOR HORIZONTAL OR VERTICAL CONTROL STATIONS. 

A, Tablet used in cooperating States. The State name is inserted at G. 
A, C, and E, Tablets for stone or concrete structures. 
F, Iron post used where there is no rock. 



Instructions to Topographers of the 
United States Geological Survey. 



HORIZONTAL CONTROL. 

GENERAL CONDITIONS. 

The boundary lines of all regular United States Geological Survey 
maps are parallels of latitude and meridians of longitude. In order 
that these shall be properly located and that intermediate points shall 
be placed in correct positions according to scale, some system of 
horizontal control is required. The method to be adopted for linear 
control should be fixed by the character of the country, the require- 
ment being that all control work shall be so accurate that no errors 
will be apparent in maps several times as large as those to be pub- 
lished. In mountainous regions or in hilly, partly timbered areas 
horizontal control is effected by a system of triangulation, the whole 
area being divided up into triangles whose apexes are represented 
by stations established on prominent points several miles apart. 
The angles between each station and all others visible from it are 
carefully measured with theodolites arranged to read angles as small 
as one second. One side of one of the triangles, called the base line, 
must be measured with great care with steel tapes, account being 
taken of slope of the line, elevation above sea, temperature of the tape, 
and other essential details, and for at least one station the exact 
latitude and longitude must be determined by astronomic observa- 
tions. 

In heavily timbered areas where it is difficult to see from any point 
more than a mile or two in any direction, horizontal control is best 



8 INSTRUCTIONS TO TOPOGRAPHERS. 

obtained from distances actually measured on the ground with 
300-foot steel tapes and angles measured with a transit at each bend 
in the line. Such control, called primary traverse, must begin and 
end at points whose positions have been previously determined, and 
be carried around the edge of each quadrangle and once across its 
center east and west. 

Because of the great expense involved in base-line measurements 
and the fixing of astronomic positions, it is generally necessary to 
connect tri angulation systems or traverse lines with positions pre- 
viously determined, even though they may be some distance away. 
There are now but few localities in the United States that can not 
conveniently be connected with known positions and distances, and 
therefore, before horizontal control work is begun, the records of the 
Coast and Geodetic Survey, the Lake Survey, the United States 
Army Engineers, and other Government organizations should be 
examined in order to ascertain what positions in the area surveyed 
have been determined and are available for use in the work on hand. 

The results of triangulation or primary traverse by the Geological 
Survey can always be obtained by anyone having occasion to use 
them by applying to the Director, United States Geological Survey, 
Washington, D, C. 

PRIMARY TRIANGULATION. 

FIELD WORK. 

On the flyleaf of each field notebook is a blank in which shall be 
recorded all information necessary to identify the book. This blank 
should be filled so far as practicable on or before the first date of entry 
of field notes, aiid it must be completely filled before the book is 
forwarded to the Washington oifice. Any failure to fill in completely 
the blank on the flyleaf of a field notebook, should be reported by 
the computer to the geographer in charge of the division. 

Personnel of party. — Each party usually consists of a triangulator 
and a recorder; also a cook and a teamster (or packer) in regions 
where camping is necessary. Additional men are required for 
heliotroping, one for each heliotrope station, and local laborers 
may be employed to clear timbered summits or to erect large signals. 



INSTRUCTIONS TO TOPOGRAPHERS. 9 

Instruments, tools, books, etc. — The following instruments and 
books are used in primary triangulation : 

One 8-inch theodolite, with leather carrying case and shoulder straps. 

Two pairs field glasses. 

One prismatic compass. 

One protractor (6-inch celluloid, full circle). 

One boxwood scale, graduated to inches and tenths. 

One 50-foot steel tape. 

One electric hand lamp. 

One 6-foot steel tape, 

Heliotropes. 

One plumb bob. 

Triangulation tablets or posts, according to requirements of country. 

Cement, cans. 

Signal notices, printed on cloth. 

Climbing irons, for use in wooded regions. 

Sun umbrellalFor use in regions where improvised sun and wind shelters 

Wind screen j can not readily be built. 

Triangulation field notes (9-912). 

Computation of geodetic distances (9-901). 

Computation of geodetic coordinates (9-902). 

Computation book, blank (9-989)- 

Nautical almanac (abridged). 

Geographic tables and formulas. 

Seven-place logarithm tables. 

A good watch must be provided by the chief of party. 

The following additional articles may be purchased in the field : 
Ax, hatchet, saw, nails, tacks, signal cloth, guy wire, stone drills 
(1^8-inch bit), drill hammer, post-hole digger, wire cutter, brace 
and bits. 

Amount of control. — At least three serviceable stations must be 
established in each quadrangle and as many more as may be nec- 
essary to afford adequate control. In addition, a number of sec- 
ondary points — such as church spires, windmills, water tanks, 
trees, and in high mountain regions some of the more prominent 
summits — must be located by intersection or by the ''three-point 
method." Where no such objects are available, at least two points 
should be flagged for intersection if practicable. These points are 
intended to afford supplementary control for the topographer and 
should be selected with special reference to their usefulness in 
that connection. 



IO INSTRUCTIONS TO TOPOGRAPHERS. 

The triangulator is also expected to locate, when practicable, 
either by direct measurement from his stations or by the three- 
point method, conspicuous objects, marks on State and county 
boundary lines, and township and section corners. Especial atten- 
tion should be given to township and section corners because of 
their recognized value in the control of the land-line net. 

Reconnaissance. — Stations should be selected and signals built 
before any observing is done, and to this end the triangulator and 
his assistant should make a reconnaissance over the area to be 
controlled. Such reconnaissance should disclose every practical 
scheme of tri angulation, the angles at each point selected being 
measured with a prismatic compass and platted with the protractor 
so that the size and proportions of the figures may be ascertained. 
All preparatory work, such as the setting of tablets and posts, the 
erecting of signals and scaffolds, and the clearing of lines of sight, 
should be completed during this reconnaissance, so that the final 
observing may be performed with economy and dispatch. The 
reconnaissance affords the triangulator opportunity to acquaint 
himself with the shortest routes of travel, with the best stopping 
places, with the available camp sites, water holes, pastures, and 
trails, and with the best routes for scaling each peak to be occupied, 
and it enables him to gain a familiarity with the special character 
of each station and its signal which will be invaluable to him in 
identifying the points when he sights them later on. 

Figures-. — The most desirable groups of triangles consist of either 
quadrilaterals with both diagonals sighted or central point figures 
with four to seven sides. The triangles composing these figures 
should be well proportioned, angles measuring not less than 30 
nor more than 120 each. The scheme should not be allowed to 
dwindle down to simple, unsupported triangles, and especial care 
should be taken to connect the work done with other work by 
means of well-proportioned triangles. Overlapping figures or an 
excess of observed lines beyond those necessary to insure a double 
determination of each length are undesirable, although an occa- 
sional diagonal through some figure may be valuable as a check. 
Additional lines of this kind only complicate the main scheme 
without materially adding to its strength, and the numerous observa- 



INSTRUCTIONS TO TOPOGRAPHERS. II 

tions made for them are discarded by the computers as superfluous . 
Judgment is to be used in this matter, however, for in many regions 
the atmospheric conditions are exceedingly uncertain and the 
topographer can not always count on being able to observe in both 
directions over every line that may be essential to the main scheme . 
In such regions it is well to err on the safe side and to obtain too 
many data rather than too few. 

Angles should be read to all prominent points outside of the area 
for use in future expansion, even though they are without signals 
or are not sharply defined. 

Secondary points. — In cutting in secondary points for topographic 
control it should be remembered that locations which depend on 
two sights only, even if the angles are of adequate size, are likely to 
be of doubtful value, because of the absence of any check on possible 
gross errors in observing or computing, or because of mistakes in the 
identification of the points. An endeavor should therefore be made 
to obtain at least three sights to every secondary point, even if the 
triangles are not of the best shape. Triangulators are especially 
cautioned not to slight the location of secondary points merely 
because they happen to be of no importance in their scheme of 
figures. The topographer may find it expedient to start his control 
from a secondary point, so that a blunder in the location of such a 
point may result in his starting with an erroneous base and having to 
make corrections at a great cost. 

Consent of owner. — Before a site for a station on private land is 
selected, the written consent of the owner should be obtained, if 
practicable, for establishing a permanent station mark and erecting 
the required signal. If a summit must be cleared of timber, or if 
lines of sight must be cut, the value of the timber to be cut should 
be definitely fixed and agreed upon with the owner before cutting 
is begun. Payments on this account should be made and sub- 
vouchers taken before the station is left. A suggested form for 
wording these vouchers is as follows: 

Received from the sum of in full payment for all dam- 
ages incident to destruction of timber on hill (or mountain), in 

County, State of , in connection with the establishment and occupation 

of triangulation station [give name of station] [date]. 



12 INSTRUCTIONS TO TOPOGRAPHERS. 

When it is necessary to clear away timber and the owner or agent 
for the ground can not be reached without great delay, three residents 
of the locality should be asked to appraise the value of the timber cut 
and to sign a written statement regarding it. This statement should 
be forwarded to the office of the Survey for consideration should a 
claim for damage be filed. 

Station marks. — Primary triangulation stations must be perma- 
nently marked by either standard iron bench-mark posts or by 
tablets, each tablet to be set in rock in place or in the top of a concrete 
or stone monument. (See second paragraph, p. 53, for instructions 
regarding the setting of tablets.) When practicable, bottles or other 
imperishable material should be left as a subsurface mark. 

Two or more permanent reference marks should be established 
about each station mark. They may consist of holes drilled in rock 
in place, spikes in roots of trees, or large stones set solidly in the 
ground. The azimuth and the distance to each reference mark 
must be duly entered in the field record. 

When old stations are revisited and any of the marks are found to 
be defective or to have been destroyed, new marks must be estab- 
lished in their place. 

Signals. — Triangulation signals must be built with a view to their 
permanence as well as to their visibility. They may be of various 
forms, the form selected depending on the locality and the materials 
at hand. Thus, a signal on a bare mountain peak may be a rock 
cairn; one on a partly wooded summit may be a straight tree, the 
surrounding timber being cleared away; one on cleared land may be 
a tripod or quadripod. 

Rock cairns should be not less than 8 feet high and should be well 
put together, so that they will withstand strong winds and heavy 
snows. A pole or a small green tree placed in the top is of advantage 
in sighting. 

Signal trees are most satisfactory if stripped of their branches, 
except a tuft at the top. They form the best of targets when sighted 
against the sky, but if they are to be sighted against a dark back- 
ground they should carry two triangular targets 3 to 6 feet on a side, 
placed at right angles to each other and covered with white cloth. 
Tripods or quadripods should be built of sawed lumber if such 



INSTRUCTIONS TO TOPOGRAPHERS. 1 3 

material is available. For the legs and center pole 2 -inch by 4-inch 
scantlings may be used, for the cross braces i-inch by 6-inch boards. 
The base of the pyramid should be large enough to permit a theodolite 
to be set up under the center pole. In order to increase its visibility, 
boards may be nailed across the sides about a foot apart and covered 
with signal cloth, and cross targets may be attached to the center 
pole above the apex of the pyramid. The best colors for this cloth- 
are white and black or white and red. 

Most signals stand in exposed places and should be securely 
anchored to prevent their being blown over. The legs of tripods 
and quadripods should be planted in the ground at least 2 feet; 
each should be fastened to a "deadman" and the holes filled with 
thoroughly tamped earth or rocks, or else a stake 4 feet long should 
be driven into the ground at an angle with each leg and firmly spiked 
to it. If the ground is too rocky to permit the digging of holes, a 
4-foot crosspiece should be nailed to each leg at right angles, flat on 
the ground, and weighted down with rocks. 

Scaffolds. — If it becomes necessary to elevate the instrument a 
scaffold must be erected in the form of a tripod, capped with a thick 
board 12 inches square, to support the instrument. Around this 
scaffold, entirely independent of it, should be built another, in 
quadripod form, supporting a platform on which the observer is to 
stand. If very high, such a scaffold should be composed of succes- 
sive bents, each 8 or 12 feet, with diagonal bracing. The outer 
scaffold, further, is to serve as a signal, and for that purpose should 
extend at least 6 feet above the observing platform and be sur- 
mounted by a mast bearing cross targets. Before fixing signals in 
position the direction in which sights are to be taken should be 
carefully ascertained, so that no woodwork will interfere with the 
observations. 

The size of the timbers to be used necessarily depends on the 
height of the structure. The amount of lumber required may be 
determined by means of a rough drawing of the structure to scale. 

Centering of signals. — Great care must be taken to insure perfect 
centering of signal and scaffold over the station mark, the plumb 
bob being used for this purpose. Signals should stand over station 
marks wherever possible, so as to avoid the necessity of computing 



14 INSTRUCTIONS TO TOPOGRAPHERS. 

swings for the angles, but if this is impracticable, as it is with a tree 
signal, then the distance and bearing of the signal to the station mark 
must be carefully measured and recorded. 

The permanent mark, tablet, or post must be the station, and when 
observations are made for angles the theodolite should be set up 
over its center if possible. If it is impracticable to center the instru- 
ment over the station mark the distance between the point occupied 
and the station mark must be carefully measured and recorded. Also 
one or more sets of angles must be read between the station mark 
and the other stations, in order of azimuth, preferably with the.o° o / 
for the pointing to the station mark. 

Heliotr oping. — The heliotrope outfit commonly used by the Survey 
is either the Steinheil heliotrope or a plane mirror with a screw 
hinged to the back to give it universal motion and improvised 
diaphragms of tin or wood with round apertures. The plane mirror 
is generally preferred to a heliotrope of the more elaborate form. 

A heliotrope is usually set up by mounting the mirror on a stake 
or board immediately over the center of the station and the dia- 
phragm on another stake, 10 or 20 feet away, which is carefully lined 
in with the distant station. The operator must constantly watch 
the reflected image of the mirror and keep it symmetrically over the 
aperture. If the sun is back of the observer a second mirror placed 
at a distance of a foot or two from the first may be used to reflect the 
light into the first. 

To the observer the flash should appear as a clearly defined point 
of light; if of appreciable size it will be necessary to bisect it, and an 
error is thus likely to be introduced. A good rule to follow is to make 
the diameter of the opening in inches equal to one-fiftieth of the 
distance in miles for work in the West, and twice this size for work 
in the East, with a minimum opening of one-quarter inch. 

Time of observing. — As a rule the best time for observing is the 
three hours before sunset; the atmosphere is then steadiest and shows 
no " boiling." The early morning hours are occasionally good but 
are likely to be less satisfactory. Many cloudy or overcast days are 
favorable. As a last resort observations at night may sometimes be 
necessary, but these require special night signals and assistants to 



INSTRUCTIONS TO TOPOGRAPHERS. 1 5 

operate them, and because of the additional cost involved are seldom 
warranted. 

Preparation for observing. — Whenever practicable the theodolite 
must be set over the station mark for reading angles, to obviate 
reduction to center, In setting up the tripod the head bolt thumb- 
screws must be left loose until the legs are firmly placed and then 
tightened. 

The instrument must be sheltered from both wind and sun. If 
the region affords no material" that is readily available for constructing 
wind screens and sun shelters a folding wind screen and a sun 
umbrella must be carried as a part of the regular outfit. 

Before observations are begun at a station all adjustments of the 
theodolite must be tested and such as are found in error must be 
corrected, special attention being paid to the micrometers to elimi- 
nate errors of run. The stations to be sighted must next be carefully 
identified by means of the directions shown on the plat or by means 
of angles previously taken with a prismatic compass. If any of the 
distant stations can not be seen with the unaided eye some object 
in line with each which can be found quickly must be selected, or, 
if necessary, the direction to each may be marked by some object 
near by, so no time shall be lost in making the pointings when the 
angles are being read. 

Method of observing. — With micrometer theodolites either single 
angles may be measured or the method of circle readings (directions) 
may be adopted. In using the latter method select for the initial 
point some station that is especially distinct and easily sighted, and 
use it as the initial point for all sets of readings. The telescope being 
set on the initial point, read both micrometers, then sight the other 
stations in succession in the order of their azimuths (clockwise rota- 
tions), closing on the initial point. Then reverse telescope, set on 
initial point, and sight the stations in reverse order. This completes 
one set of readings with telescope direct and reversed. Now shift the 
circle about 36 (examine the plate bubbles after this shift and relevel if 
necessary) and commence another set. When pressed for time it is 
advisable to shift the circle when telescope is reversed. No angle 
should be considered as well determined that has not been meas- 
ured on at least 5 different parts of the circle or 10 times in all, 5 



1 6 INSTRUCTIONS TO TOPOGRAPHERS, 

with telescope direct and 5 with telescope reversed. When the 
telescope is reversed each end of its a£is will rest in the same Y as 
before. Reversals are of especial importance when there is an ap- 
preciable difference in the elevations of the points sighted. 

If the observations are made in the afternoon it is advisable to 
take all secondary pointings before commencing the observations 
to stations, and there should be at least two sets of such pointings: 
the remaining time for observing can then be devoted to the accu- 
rate measurement of the important angles while conditions are 
the most favorable. 

The graduated circle should never be placed so that when pointing 
at any particular station the micrometers will be set to even degreer 
except, as before noted, while data are being obtained for ''reduc- 
tion to center." 

Field record. — The field record is to be kept in book 9-912. It 
must be written in a plain, neat hand, with a No. 4 pencil, or with ink 
and no part of it must on any account ever be erased. A single line 
should be drawn through erroneous records, the corrected figures 
being written above. If deemed necessary an explanation should 
be written in the column for remarks. The memory should not be 
trusted for data of any kind; the record must be faithfully kept in 
all particulars and be made so complete that it can be understood 
by another person at any time. 

The flyleaf of each notebook must be properly filled in when the 
book is first used and one of the blank flyleaves must contain an 
index of the contents. 

The date, name of station, time of observing, and names of ob- 
server and recorder should be systematically entered at the head 
of each page. 

The position of the instrument with respect to the center of the 
station must be clearly defined and if it is set up off the center a 
full statement must be given of the distance and the angles measured. 

On the page immediately preceding the record of angles should be 
written a minute and complete description of the station occupied, 
the station marks, character of signal, nearest camping or other stop- 
ping places, roads, and trails, also a statement regarding the own- 
ership of the land and such other information as will be helpful to 



INSTRUCTIONS TO TOPOGRAPHERS. 1 7 

the topographer. The description must be written before the re- 
corder leaves the station and should be accompanied by a rough dia- 
gram showing directions to other stations and plan indicating loca- 
tion of instrument if it was not centered on the station. 

Inasmuch as station names are to be published, effort should be 
made to select names that have local significance. 

Reading and recording of Angles. — When the micrometer wires &e 
set for a reading with the Geological Survey theodolites it is very 
important that the last movement of the wires be tow r ard the right. 
The readings on the graduated head are then decreasing and the 
spring attached to the slide which holds the wires is being com- 
pressed. If the cross wires are moved the least bit too far to the 
right they must not be turned backward to the setting but must be 
turned backward at least a halfturn of the screw, then brought for- 
ward slowly to a correct setting. When the setting is properly made 
a division on the graduated plate will appear exactly midway be- 
tween the two movable cross wires and an equal amount of white 
space will show on each side of it. A part at least of the micrometer 
adjustment errors can be eliminated by making the settings with 
less than five turns of the screw; this can always be done if the right- 
hand part of the comb scale is sometimes used for comb scale and 
micrometer head readings, the io-minute space being taken from 
the left. 

For all precision instruments where a tangent screw and spring 
are used together, the setting should be made while the spring is 
being compressed, otherwise the "slack" of the screw may cause 
an error. 

The recorder should not only take down the readings called off 
by the observer but should without delay compute the angles be- 
tween successive stations and also the mean readings. The following 
form is to be used for recording angles by the method of directions: 
8221 — 11 2 



i8 



INSTRUCTIONS TO TOPOGRAPHERS. 



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INSTRUCTIONS TO TOPOGRAPHERS. 19 

Opposite each angle record any necessary information as to visi- 
bility of signals or atmospheric conditions. 

Field computations. — Angles at each station should be reduced to 
center in the field in order to test the triangle closures, which for a 
primary scheme should not exceed five seconds. 

Arbitrary adjustments and preliminary computations of positions 
should also be made in the field. Book 9-889 is to be used for sum- 
mary of angles and for miscellaneous computations. Computations 
for distances should be entered in book 9-901 and for coordinates in 
book 9-902. For field computations of coordinates where the lines 
are short five or six place logarithms will give sufficient accuracy and 
the computations may be shortened by omitting some of the minor 
corrections, carrying results to tenths of seconds of latitude and 
longitude only. 

Triangulation plot. — A careful plot of the work should be kept on 
the scale of 10 miles to an inch, and each month a reduced copy, on 
which angles measured are indicated by the usual sign, should be 
sent in on the monthly-report blank. The plot, if carefully made, 
will prove invaluable for finding directions to distant stations. Place 
the protractor on the plot with o° in line with a station that can be 
seen clearly, then read in turn the angle to each other station, thus 
obtaining an observing list. 

Azimuth observations . — There must be not less than two azimuth 
stations in each triangulation scheme, but if the azimuth of any line 
in a scheme can be computed from former observations then only one 
azimuth station need be established for each square degree controlled. 

The azimuth mark should be placed at least half a mile from the 
station. It should consist of a vertical slit one-fourth to one-half 
inch wide and 6 inches long, cut in a small box containing a candle 
or lantern. To illuminate the cross wires of the instrument and to 
read the angles, an electric hand lamp is to be preferred. 

The observations should consist of not fewer than five direct and 
five reversed measurements between the star and mark. As the 
star is at a much higher angle of elevation than the mark it is impor- 
tant that the horizontal axis of the theodolite be adjusted with care 
and leveled. The ends of the striding level bubble must be read at 
each setting on the star and a level correction computed if there is 
an appreciable difference between them, as shown in the example 
attached. 



20 



INSTRUCTIONS TO TOPOGRAPHERS. 



Observations on Polaris should be made immediately preceding 
and following elongation, as any error in the time of observation has 
then the least effect on the resulting azimuth. The time of setting 
the cross wires on the star must be recorded to the nearest second. 
The watch error must be known and to this end the triangulator 
should compare his watch frequently with telegraphic time, which 
is sent over Western Union lines once a day, usually at noon Wash- 
ington time. 

Example of record of azimuth observations. 

Station: Canada, Ky. 8-inch theodolite No. 434. One division of micrometer= 
2". One division of level=2" of arc. June 11, 1910. Watch o m 23 s60 slow. 

Telescope direct. 



Object. 


Time a.m. 


I^evel. 


Micrometer. 


Mean. 


Angle. 


West. 


East. 


A. 


B. 


Mark 


H. m. s. 


Div. 


Div. 


' div. 
352 54 09 
288 35 24 


' div. 
172 53 21 
108 35 05 


/ // 

172 54 00 
108 35 29 


/ it 


Polaris 


2 30 50 


11. 
9.0 


10. 
12. 










64 18 31 






!. O 















Telescope reversed. 






Mark 








172 53 04 
10S 34 10 


352 52 13 
288 33 27 


352 52 47 
288 34 07 




Polaris 


2 36 48 
2 40 26 


11. 
9.0 

20. 

10. 
10. 


10. 
12. 






22. 

J.O 

II. 
II. 


64 18 40 


Polaris 

Mark 


202 41 13 
138 22 24 


22 40 22 
318 22 06 


22 41 05 
318 22 30 










20. 


22.0 
\. 


64 18 35 











Telescope direct. 



Mark . . . 
Polaris. 



2 46 52 



10. o 
11. o 



II. o 

10. o 



O 21. O 
O.O 



22 41 07 
318 22 20 



202 40 17 
I38 22 13 



202 40 54 
138 22 33 



64 l8 2] 



Note. — Four other sets should be taken. 



INSTRUCTIONS TO TOPOGRAPHERS. 21 

COMPUTATIONS. 

Preliminary computations of distances from unadjusted angles 
should be made in the field as required by the rule on page 10. 
The steps in the final adjustment and computation are as follows: 

i. Computation of mean angles. 

2. Closing the horizon. 

3. Tabulation of angles. 

4. Reduction to center. 

5. Tabulation of triangles which form geometric figures. 

6. Computation of spherical excess. 

7. Formation of side or sine equations. 

8. Formation of equations of condition. 

9. Formation of table of correlates. 

10. Formation of normal equations. 

11. Solution of normal equations. 

12. Substitution of corrections. 

13. Correction of tabulated angles and sines. 

14. Distance computation. 

15. Computation of geodetic coordinates. 

16. Tabulation of results. 

Operations 1 and 2 are completed in field record book 9-912; 3 to 
5 and 7 to 13, inclusive, in book 9-889; 6 and 14 in book 9-901; and 
15 in book 9-902. The results are tabulated on printed blanks 8 
by 10X inches in size, one blank for each station. 

Closing the horizon. — In careful work closing errors will always be 
small and may be distributed among the various angles in propor- 
tion to their number. If there are any angles measured which should 
equal the sums of smaller angles, proper corrections must be made 
before the horizon is closed. 

For convenience of reference a rough plot should be made for each 
station on part of a page in book 9-889, showing relative size and 
position of the various angles with names of stations sighted, and 
on the same or the following page should be given a summary of all 
the angles at the stations, in order of azimuth, with the angles and 
distances to signals for eccentric stations. 

Reduction to center. — For eccentric stations the data for reduc- 
tion to center should be indicated on the plat and figures given for 
them in the summary. An illustration of the method of procuring 
these data is given below. (See also fig. 1, p. 24.) Two sets of 
angles were read at Elk station (where an eccentric point was occu- 
pied), with one of the micrometers set very nearly on o°, when the 



22 



INSTRUCTIONS TO TOPOGRAPHERS. 



telescope was pointing directly toward the center of the signal. 
The angle to each point in turn is given below. By measuring the 
angle with this setting the computer is saved considerable trouble, 
and the possibility of error is lessened. The measured distance be- 
tween the center of the instrument and the center of the station 
was 4.7 feet (1.43 meters). 
The formula for computing the swing in seconds for any line is — 
Distance to signal sin angle signal to far station 



•X 



Distance to far station 



The distance to signal will be a constant for each set up, hence its 
logarithm may be combined with the sine of 1 second and this con- 
stant used throughout the computation. The distances to the 
distant stations in logarithms of meters are derived from a prelimi- 
nary computation. 

log 1.43 =0.15534 

log sin 1" =4.68557 

log constant = 5. 46977 

ELK STATION. 



Station 

Angle 

Log constant 

Log sin angle 

A. C. log distance 

Log correction 

Correction in seconds 



Dick. 



23 07 10 

5-46977 
9. 59400 
5- 70154 



o. 76531 

+ 5.83 



Taylor. Browning. Tweedy. 



68° 43' 40" 

5- 46977 
9-96935 
5- 59196 



1. 03108 
+ 10.74 



109° 16' 54 

S-46977 
9- 97493 
5- 7478i 



1.19251 

+ 15-57 



206 27' 10" 

5-46977 
9. 64881 
5-63275 



o. 75133 

-56.41 



The sign for any correction is the same as that for the sine of the 
angle, therefore for an angle over 180 it will be negative. 

The correction for any angle will be the difference between the cor- 
rections for the two lines bounding it, always taking the lines in 
order of azimuth. Thus, for Dick-Elk-Taylor it will be — 

+ 10.74 
- 5-83 



+ 4- 9i' 



For Browning-Elk-Tweedy it will be — 



—56.41 

-15-57 



-71.98" 



INSTRUCTIONS TO TOPOGRAPHERS. 23 

The general rule is, change the sign of first correction (in order of 
azimuth) and add algebraically to the second correction. The sum 
will be the correction to the angle. The angles listed on page 25 
have all been corrected. 

The foregoing formula may be used also when it is desired to com- 
pute the " swing* ' for a line, which is to be applied at a distant sta- 
tion to change the pointing to the marked point— that is, the station 
center — from that taken to the signal. Whether the computed swing 
is to be added to or subtracted from a given angle may easily be 
found by an inspection of the diagram. 

Formation of triangles. — By an inspection of the field plat of the 
triangulation determine what groups of triangles are so interrelated 
that a change in one will affect the others and what groups of tri- 
angles should be adjusted as a unit. For the triangulation by the 
Geological Survey, which is not executed for geodetic purposes, it 
is not advisable ever to include more than 15 or 20 triangles in such 
a group, because the labor of solving equations for the adjustment of 
any group increases rapidly with its size. 

Four overlapping triangles form the simplest group that may be 
adjusted by the usual least-square methods. 

Assume the group shown in figure 1 for adjustment. Tabulate 
the angles for each triangle, as shown at (a), (b), (c), and (d) (p. 25). 
Any angle in any of these triangles may be considered as the difference 
between the azimuths (directions) of its two sides. For example, 
angle Dick-Elk-Taylor, or 3.0.2, using for convenience the figures 
assigned to each angle vertex, would be the azimuth or direction 
of the line 3-0 subtracted from the azimuth or direction of the line 
2-0. Azimuths are always measured in a clockwise direction. 
Therefore this angle may be indicated as —3.0+2.0 or —3/0+2/0. 
In the latter form the denominator is always the figure at the vertex 
of the angle and with the vertex pointing toward the observer the 
left-hand direction is always given the minus sign. (Directions 
will hereafter be referred to as sides.) 

Spherical excess. — For any triangle on the earth's surface the sum 
of the three angles, if correctly measured, will exceed 180 by an 
amount varying with the area. For considerable areas the observed 
angles must be reduced to their plane values by deducting one-third 



24 



INSTRUCTIONS TO TOPOGRAPHERS. 






the spherical excess from each. The spherical excess for any tri- 
angle between latitude 25 and 45 ° is approximately 1 second for 
each 75.5 square miles of area, or exactly equals in seconds ABra sin 
C, in which A, B, and Care respectively the lengths of the two sides 
in meters and the included angle of any triangle, and m is a constant 
depending on the latitude. The logarithms of m are given on page 
271, "Geographic tables and formulas." In computing spherical 
excesses for any figure (as that on p. 25 and fig. 1, for example) 
arrange the work systematically, the logarithms of each of two sides 
in meters from a preliminary computation, the logarithm of the 



Taylor 



Dick 




Browning 



Elk 



Figure i, 



sine of their included angle, and the logarithm of m for the mean 
latitude for each triangle; place in a column. Give the figures for 
the triangle at the head of the column, as 3.0.2, using the angle 
3.0.2 and the sides 3-0 and 2-0 in the computation. 



Triangles. 




Log side A 
Log side B 
Log sin C. . 
Log m 



Log spherical excess 

Spherical excess in seconds 



Mean latitude, 37 35' 



4. 40804 
4.25219 
9. 81304 
1, 4047s 



9. 87802 
o. 76 



INSTRUCTIONS TO TOPOGRAPHERS. 



25 



In the same manner the spherical excess for each of the remaining 
triangles is computed. 

As the spherical excess for a given area is constant, the sum of the 
spherical excesses for the triangles 2.0.1 and 3.0.2 must equal the 
spherical excesses for the other two. This check should always be 
applied to the results. In many cases it will be convenient to 
perform this computation in the book (9-901) used for preliminary 
distances, in the left-hand column adjacent to each triangle. 

Angle equations. 



Stations. 



(Elk 

(a K Browning 
[Taylor. . . . 



(Elk 

(bKTaylor.. . 
[Dick 

(Elk 

(cK Browning 
[Dick 

(Dick 

(d)l Browning 
[Taylor . . . 



Side. 



— 2/0+1/0 
— 0/1+2/1 

— 1/2+0/2 



•3/0+2/0 
•0/2+3/2 
■2/3+0/3 



—3/0+1/0 
-0/1+3/1 

-1/3+0/3 



-2/3 + 1/3 
-3/1+2/1 
— 1/2+3/2 



Observed 
angle. 



40 33 19. 17 
95 23 07. 62 
44 03 30. 52 



i79 59 57-31 

.76 



Error —3-45 

45 36 34- 90 
50 34 37-57 
83 48 53- 15 



180 00 05. 62 
.92 



Error +4. 70 

86 09 54. 07 
50 10 30. 58 
43 39 38.99 



180 00 03. 64 
.90 



Error +2. 74 

40 09 14. 16 
45 12 37.04 
94 38 08. 09 



179 59 59- 29 
.78 



Error —1. 49 



Correc- 
tion. 



+ 2. 12 
+ .71 
+ .62 



2.97 
.40 

1-33 



.84 

1.47 

•43 



— .90 

+ 2. 18 
+ .21 



Corrected 

spherical 

angle. 



40 33 21. 29 
95 23 08.33 
44 03 31. 14 



180 00 00. 76 
Spherical 
excess. . o. 76 



45 36 31-93 
50 34 37- 17 
S3 48 5i- 82 



180 00 00. 92 
Spherical 
excess. . o. 92 



86 09 53. 23 
50 10 29. 11 
43 39 38. 56 



180 00 00. 90 
Spherical 
excess.. 0.90 



40 09 13. 26 
45 12 39. 22 
94 38 08. 30 



180 00 00. 78 
Spherical 
excess . . o. 78 



26 



INSTRUCTIONS TO TOPOGRAPHERS. 

Sine equation. 






Sides. 


Angle. 


Sine. 


Differ- 
ence for 

1". 


Correc- 
tion in 
seconds. 


Cor- 
rection 
to sine. 


Corrected 
sine. 




f f-2/3+0/3 

+{-2/0+1/0 

I-3/1+2/1 

(—2/3+1/3 
— s— 3/0+2/0 
I I-0/1+2/1 


83 48 53- 15 
40 33 19- 17 
45 12 37.04 

40 09 14. 16 
45 36 34- 90 
95 23 07.62 


9. 9974645 
9- 8130350 
9. 8510731 


+02. 2 
+24.6 

+ 20. 9 

+24.9 
+ 20. 6 
— 2. 


-i-33 
+2. 12 
+ 2.18 

— -91 
-2-97 
+ .71 


— 3 
+ 52 
+46 

-23 
-61 

— 1 


9. 9974642 
9. 8130402 
9.8510777 


(e) 


9. 6615726 

9. 8094543 
9- 8540576 
9. 9980787 


9. 6615821 

9. 8094520 
9.8540515 
9. 9980786 




9. 6615906 
Error —180 


9. 6615821 



Equations of condition. 



(f) o=— 3.45"— 2/0+1/0— 0/1+2/1 — 1/2+0/ 2 

(g) o=+4- 70"— 3/0+2/0— 0/2+3/2— 2/3+0/3 
(h) o=+2. 74"— 3/0+1/0— o.'i +3/1 — 1/3+0/3 

{o=— 1.80"— .022 2/3+. 022 0/3—. 246 2/0+.246 1/0— .209 3/1+.209 2/1 + . 249 2/3 
— . 249 1/3 + . 206 3/0—. 206 2/0—. 020 0/1 + . 020 2/1 
o=— 1. 80"+. 227 2/3 + . 022 0/3 — .452 2/0+. 246 1/0— . 209 3/1+. 229 2/1 
— . 249 1/3 + . 206 3/0— . 020 0/1 



Table of correlates . 



(j) 


(k) 


(1) 


(m) 


(n) 


Correlates after substituting computed values. 


Sides. 


1 


2 


3 


4 


1 
+0.275 


2 
—0. 063 


3 
—0. 589 


4 
+3-O07 


Correc- 
tions. 


Sides. 


1/0 
2/0 
3/o 
0/1 
2/1 
3/1 
0/2 
1/2 
3/2 
0/3 
i/3 
2/3 


+1 

—1 

—1 
+1 


' + i' 

— 1 


+ 1 

— 1 

— 1 


+0. 246 

— -452 
+ . 206 

— .020 
+ - 229 

— . 209 


+0.275 

— .275 

— .275 
+ .275 


—0. 063 
+ .063 


-O. 589 

+ '.'589' 
+ .589 


+0. 740 
— 1-359 
+0.619 
—0. 060 
+0. 689 
— 0. 628 


+0.426 

— 1.697 
+ 1.271 
+0.254 
+0.964 

— 1. 217 
+0.338 
—0.275 
—0. 063 
-0. 586 
— 0. 160 
+0. 746 


1/0 
2/0 
3/o 
0/1 

2/1 
3/ 1 

0/2 

1/2 

3/2 
0/3 

1/3 

2/3 




+ 1 




- .589 


+ 1 
—1 


— 1 


+ -275 
— -275 


+ .063 










+ 1 
+ 1 






— .063 

— .063 






+ 1 
— 1 


+ .022 
— .249 
+ .227 




- .589 
+ .589 


+0. 066 
-0. 749 
+0. 683 




— 1 




+ .063 



INSTRUCTIONS TO TOPOGRAPHERS. 



27 



(o) Normal equations. 



I 


2 


3 


■ 4 


Absolute 
term. 


+ 6.000 


— 2 . OOO 

+ 6. 000 


+ 2. OOO 

+ 2.000 
+6.000 


+ 0-947 
-0. 863 

+0. 122 
+ 0.51779 


—3-450 
+4- 700 
+ 2. 740 
— 1. 800 















Solution of equations, 
(p) Normal equations. 



(Pi) 

(P2) 

(P3) 
<P«) 

(P5) 
(P6) 

(P7) 



+ 6.000 
(• 1667) 



— 2.000 
+ -333 



+ 5-333 
(•1875) 



+ 2.000 

— -333 

+ 2.667 

— .500 



(.250) 



4. OOO 



-1-0.947 

- .1578 

— -5473 
+ . 1026 

+ .0800 

— . 0200 



+ .31060 
(3.2196) 



Absolute 
term. 



—3-450 
+ -575 

+3-55Q 

— .666 

+ 2. 115 

— -529 

— -934 

+ 3.007 



(q) 





2 


3 


4 


Absolute 
term. 


(qi) 
(q 2 ) 


+ 6. coo 
- .667 


+ 2. 000 
+ .667 


-0. 863 

— -3157 


+ 4- 700 
-1. 150 


(q 3 ) 
(Q4) 




+ 6. 000 
- .667 


+ . 1220 
— -3157 


+ 2. 740 
+ 1-150 


(qs) 




— 1-333 


+ -2737 


-1-775 


(qe) 






+ .51779 


— 1. 800 


(qr) 
(qs) 
(q 9 ) 






— . 14944 

— .05615 

— . 00160 


+ -544 
+ -364 
— . 042 



(r) 





« 


2 


3 


4 


(n) 
(r 2 ) 
(r 3 ) 

M 

(r 5 ) 


+0.575 

- -475 
. 196 

— .021 

+ -275 


-0. 666 
+ -309 
+ .294 

- .063 


—0. 529 
— . 060 


+ 3.007 


- .589 



28 INSTRUCTIONS TO TOPOGRAPHERS. 

Least-square adjustment. — After deducting the spherical excesses 
from the sums of angles for each triangle (a), (b), (c), (d), page 25, 
the differences between the remainders and 180 will be the errors, 
plus for remainders over 180 and minus for those less than 180 . 

The rules for determining the number of angle equations and 
the number of sine or side equations required for the proper adjust- 
ment of any figure are these : 

L— S+i= angle equations 
Iv— 28+3= sine equations 

Where 1^ equals number of lines in the figure and S the number of 
stations. A solution of these equations for a quadrilateral shows 
that three angle equations and one side equation are required. 
In the present example it is immaterial which three triangles are 
used for the adjustment. 

To select the sines for the side equation: Consider the figure 
as a pyramid with vertex at 2; by redrawing the figure with the 
line 3-1 dotted and the triangle 2-3-0 shaded, it will appear to 
the eye as such a pyramid. Select for the first set of angles for the 
sine equations those opening to the front in going around the base 
of the pyramid from 3 to o to 1 to 3 ; mark them with solid arcs of 
circles; the remaining angles around the base make up the other 
set and are marked with dotted arcs. In selecting the point for 
the vertex of the pyramid, as a general rule choose the one which 
includes the smallest angles, but if all the angles are greater than 
30 either station may be chosen. Find the sines for each set of 
angles, recording also the differences for 1" for each; call the first 
set of sines plus and the second set minus, find the difference between 
them, and give it the sign of the greater. 

Equations of conditions are now made up as follows: For triangle 
(a), error equals —3. 45"; this is made up of the errors in the azimuth 
or pointing of the sides —2/0+1/0 — 0/1 + 2/1 — 1/2+0/2, six in all. In 
like manner form equations (f), (g), and (h). The sine equation (i) 
is made up as follows: The error of the sines, being the difference 
between the two sets, is —180. To correct the sines, changes in 
seconds to be found for the angles must be multiplied by the differ- 
ences for 1" in column 4 of (e) for the given angle; hence for the first 
sine this will be +2.2 multiplied by the corrections to be given the 
directions —2/3 and +0/3, or if expressed in a simple form it will 
be —2.2 2/3+2.2 0/3. Treat each side and difference for \" in like 



INSTRUCTIONS TO TOPOGRAPHERS. 



29 



manner, noting, however, that for the second set of sines, which is 
considered negative, each sign given for the side will be reversed; 
for example, the first one is written +24.9 2/3—24.9 1/3. It will be 
noticed that in the first form of (i) as written, 2/1 appears twice with 
like signs, 2/3 appears twice with unlike signs; combine like terms 
algebraically, thus reducing the equations to the second form of (i;. 
For the convenience of the computer and in order to avoid the han- 
dling of large numbers, both equations (i) have been divided through 
by 100; this, of course, does not alter their value. 

There are now four equations to be solved and twelve unknown 
quantities; the latter are combined and reduced to four in the table 
of correlates. Column (j) contains the marks for the sides or direc- 
tions for which corrections are required. Column (k) contains on 
the proper lines the algebraic coefficients for the various sides from 
equation (f); for example, —2/0, considered as a quantity, might be 
written — 1 (2/0), and +1/0 in like manner written +1 (1/0) — 1 and 
+ 1 are therefore the entries for column (k), lines 2/0 andi/o. 

The formation of normal equations from the table of correlates is 
as follows: Column 1 of (o) contains the sum of the squares of each 
quantity in column (k). Column 2 contains, first, the product of 
each quantity in column (k) by corresponding quantities in column 
(1); second, the sum of the squares of each quantity in column (1). 
Column 3 contains the sum of the products of (k) by (m), (1) by 
(m), and (m) by (m) (the squares). Column 4 is made up in same 
manner, using the quantities and signs as given. If columns 1, 2, 
and 3 were completely filled out by products found as indicated 
above, it would be found that the quantities from +6.000 down the 
column would be the same as those from +6.000 along the lines to the 
right to column 4. But as the former are not needed in the solution 
they have been omitted; had they been retained the equations in 
full would be as follows, the second member of each equation being 
zero: 

Normal equations. 



I 


2 


3 


4 


Absolute 
term. 


+ 6. 000 
— 2. 000 
+ 2. 000 
+ -947 


— 2. 000 
+ 6. 000 
+ 2. 000 

- .863 


+ 2. 000 
+ 2. 000 
-f- 6. 000 
+ . 122 


+0. 947 
- .863 
+ . 122 
+ .51779 


—3- 450 
+ 4. 700 
+ 2. 740 
— 1. 800 



30 INSTRUCTIONS TO TOPOGRAPHERS. 

These are ordinary algebraic equations which may be solved by 
the usual rules of algebra, but as the solution of 5, 10, 15, or more 
equations is often required in Geological Survey work the process 
should be conducted systematically as shown. 

The first normal equation is written in full on line (pj), parts of 
the other equations are written on lines (q^, (q 3 ), and (q 6 ). The 
reciprocal from Barlow's tables of the first quantity (+6.000, line 
(pj), column 1), is placed at the left. The product of this reciprocal 
(0.1667) by the quantities on line (pj), columns 2, 3, and 4, and 
absolute are written immediately under each in turn; the quantity 
+0.333 (line (p 2 ), column 2) is now used as a multiplier for line (p 2 ) 
(omitting column 1), and the products are placed in columns 2, 3, 4, 
and absolute, line (q 2 ); in like manner the quantities —0.333 (column 

3, line pi) and —0.1578 (column 4) are used as multipliers and the 
products written on lines (q 4 ) and (q 7 ). The algebraic sums of lines 
(q^) and (q 2 ) are now written on line (p 3 ), which is then used as if 
it were an original equation. The reciprocal of +5.333 is found and 
used as a multiplier as before and the products written on line (p 4 ). 
The next products are written on lines (q 5 ) and (q 8 ). The sum of 
each column of lines (q 3 ), (q 4 ), and (q 5 ) is carried over to (p 5 ). The 
process is repeated for each equation until finally the product 
+3.007 is found, which is the value for unknown quantity numbered 

4. This value and also the quantities in the column of absolute 
terms, lines (p 6 ), (p 4 ), and (p 2 ), are copied in table (r), line (r t ). 
With +3.007 as a multiplier products of each quantity in column 4, 
lines (p 6 ), (p 4 ), and (p 2 ), are found and written on line (r 2 ), columns 
3,2, and 1. Column 3 of (r) is then summed and the result ( — 0.589) 
is the value of unknown quantity numbered 3. This is used as a 
multiplier and products found with quantities from columns 3 and 
2, lines (p 4 ) and (p 2 ), and in like manner values for unknown quan- 
tities numbered 2 and 1 are found. 

The solution of the normal equations and the values found for the 
unknown quantities may be checked, if desired, by substituting in 
the full equations, page 29, but usually an experienced computer 
will not need to undertake this extra work, depending rather on the 
accuracy of his results until checked by use as correction in the 
original triangles, (a), (b), (c), and (d), and in the sine equation (e). 



INSTRUCTIONS TO TOPOGRAPHERS. 3 1 

The next step in the adjustment is to substitute the values for the 
four unknown quantities in the tables of correlates and to find the 
correction for each side. The method of doing this can be easily 
seen by following the process through the right-hand half of that table . 
For convenience, the value found for each unknown quantity is 
written at the head of columns 1,2,3, and 4. Each of these in turn 
is multiplied by quantities in columns 1, 2, 3, and 4 of the left-hand 
part of the table and the products are placed in the right-hand part on 
the same line with the multiplicand . The final correction for any side 
is then the algebraic sum of the quantities which are on line with the 
side number in columns 1,2,3, and 4 (at the right side of the table). 
Thus the correction 1/0 is made up of +0.275, —0.589, +0.740 = 
+0.426; this is the correction in seconds to the side. The correction 
for any angle, then, is the difference between the corrections for the 
two sides bounding it. For example: Angle at Elk, triangle (a), is: 

— correction 2/0 = + 1.697 
+ correction 1/0 = -{- .426 



-1-2. 123 

The correction for any sine is the correction for the corresponding 
angle multiplied by the difference for iff in the sine. 

It is desirable to have triangles close without errors greater than 
a hundredth of a second and sine equations close to the seventh 
place of logarithm, but unless the normal equations are carried to 
three or four decimal places, there will possibly be residual errors 
of two or three hundredths in some triangle closures. It is, however, 
considered allowable to make arbitrary changes of not over zbo.03" 
in angles in order to procure consistent results. 

Large figures. — Generally adjustments must be made of figures 
larger than quadrilaterals. The equations on page 28 show how 
many angle and sine equations are required for any figure. By 
inspection, large figures may be divided into simple groups, each 
line of which must be a necessary part of a pyramid, as suggested 
on page 28. The number of pyramids will be the same as the number 
of sine equations, and no more. Select from each pyramid group the 
triangles which would be used in adjusting that group alone, remem- 
bering that triangles so selected must always cover the given area 
once, but never the entire area twice. After making up a series 
of sine and angle equations in this manner, if any triangle appears 



32 



INSTRUCTIONS TO TOPOGRAPHERS. 






in several groups, omit each duplication of it, checking the final 
number retained by the formula. It is sometimes advisable to 
omit a long, unimportant cross line in a large figure rather than 
increase the labor of adjustment by retaining it. When loss of 
accuracy will not result, groups of triangles should be adjusted as 
units which will not require more than 8 or 10 normal equations. 
For United States Geological Survey work groups involving over 
15 equations should not be undertaken. 

Weighted adjustments. — In order to adjust as a whole an extensive 
triangulation scheme, the strongest groups are adjusted first; then 
if lines or triangles in them form parts of other groups, their first 
adjusted values are given infinite weights and thus left unchanged. 
Weights if used in an adjustment appear in the table of correlates 
only. For any side they are used by inserting them in an extra 
column in the table (this would be placed between (j) and (k) if 
used in the present example). The weight for a side taken as a 
whole number 1, 2, 3, etc., or 00, is written on the line with the 
side number. Any product with quantities on that line in either 
the right or the left side of the table is divided by the corresponding 
weight before it is used in any way; where 00 is used this results 
in canceling all of the corresponding . products — in other words, 
the side may be omitted. 

Computations of distances. — These are to be made in book 9-901 . 
The triangles are arranged in order from a given base or known side, 
one page or part of a page being taken for each new station. For each 
triangle the adjusted spherical angles and the spherical excess are 
given to hundredths of seconds. 



Station. 



Browning. 

Elk 

Dick 



Miles, 16.827, Browning to Elk . 
Miles, 24.319, Browning to Dick 



Spherical 
angle. 



50 10 29. 11 

86 09 53- 23 
43 39 38. 56 



Spherical 
excess. 



0.30 
•30 
•30 



180 00 00. 90 180 00 00. 00 



Plane angle. 
9.8853615 



50 10 28. 81 
86 09 52. 93 
43 39 38. 26 



Log sines 
and dis- 
tances. 

4.4789254 



o. 1 146385 
9. 9990263 
9.8390017 



4.4326556 
4. 5925902 



INSTRUCTIONS TO TOPOGRAPHERS. 



33 



The rule for the solution of plane triangles for which the three 
angles and one side are given is that the sides are proportional to the 
sines of the opposite angles. By always arranging the angles in the 
above form with the new station first, the solution is made somewhat 
mechanical. The logarithms of the sines of plane angles are, of 
course, used; that for the angle at the new station from which dis- 
tances are required to the other two stations is written immediately 
above the angle; its arithmetical complement (10 minus the sine) 
is written to the right and on line with the angle. Each of the other 
sines is placed on line with the angle to which it relates. Imme- 
diately above the sines is written the logarithm of the distance in 
meters between the second and third stations in the triangle; in the 
example this is 4.4789254 for the line Elk to Dick. 

To get the logarithm of the distance from the new station (Brown- 
ing in the example) to one of the other stations, omit the sine opposite 
the latter and add together the remaining logarithms in the right- 
hand column. The distance to thousandths of a mile for each com- 
puted line must be found and placed to the left of the names of the 
terminal stations. The work should be verified by comparing dis- 
tances for each line that has been computed from two or more 
triangles. 

Computation of geodetic coordinates. — For this work use book 9-902 
and check results by computing each position from the two stations 
which form a triangle with the new station. For convenience, only 
one of the computations is here given : 

o / // 

Azimuth a: Elk-Dick q6 56 01.12 

Spherical angle at Elk 86 00 53. 23+ 

Azimuth a': Elk-Browning 183 05 54. 35 

Aa-f 180 180 00 36.47 

Azimuth (a): Browning-Elk 3 06 30.82 

Geodetic Coordinates. 

LATITUDE. LONGITUDE. 

o r n or// 

37 28 47.32 Elk. X 82 00 16. 16 

Af... 14 37- x>(+) A A 50. 77(~) 

<£' 37 43 24.42 Browning. X f 81 50 16. 3Q 

8221 — 11 3 



34 



INSTRUCTIONS TO TOPOGRAPHERS. 



Geodetic Coordinates— Continued. 



Computation for latitude: 

logs 4.4326556 

log B 8. 5110415 

log cos a' . . . 0. 9Q93^47(—) 



log (I) 2.Q43o6i8(-) 

logs 2 8.86531 

logC 1-28943 

log sin 2 a'... 7.46561 



A arc and sine 
(log s) —13 
(log V) +00 

-13 



log (II) 7-62035 

log D 2. 3771 

log[I + II] 2 .. 5.8861 



<f> 37-28-47. 3 
#37 43 24.4 



72 11. 7 
37 36 06 



log (III) 



?. 2632 



log E 6. 0528 

log s 2 sin 2 a' . 6. 3309 
log (I) 2.943i(-) 



-log (IV)... 5-3268(+) 

Computation for latitude 

<D 8 ? 7.i26(~) 

(II) 004 + 



(III). 
(IV). 



.018 + 
.ooo(+) 



877- 10 4(~) 



[I+II] 877-122 
log [I+II] 2. 94306 

log [I+II] 2 5.88612 



Computation for longitude: 

logs 4.4326556 

log sin a' 8. 7328074^) 

log A' 8. 5091756 

log sec 0' 0. 1018382 



A a and s 



(-13) 



log(V) i.7764755(~) 

59. 769- 
A-* 59-77- 

Computation for azimuth: 

log(V') i. 7 76476(-) 

/<£+0'\ 
log sin \—^-) 9-785450 

log sec ( ^ ^ \ 0. 000000 



log (VI) I.s6i926(-) 

-Aa 36".47(+) 

Azimuth check. 

o / // 

53 16 59- 9 4 
3 06 30. 82 

Check: 50 10 29. 12 

Spherical angle 
at Browning 50 10 29. 11 



-A0 I4 37-M+) 

Computation of Azimuth a, in Book 2752, page 21. 

Spherical angle and distance=s, in Book 2751, page 9. 

Computed by E. M. D. 

[Note. — logarithms marked + or — are found from the signs of the cosine and 

sine of azimuth.] 

In this example the azimuth at the top of the page is derived 
from a previous computation. The spherical angle is that at Elk 
from the adjusted figure. Whether to add or subtract this can be 






INSTRUCTIONS TO TOPOGRAPHERS. 35 

determined very easily by inspecting a plat of the stations, but 
when for one of the pair of computations the spherical angle is 
added, the other is always subtracted. The latitude and longitude 
at Elk are also derived from a previous computation. Logarithm 
s is the logarithm of the distance in meters between Elk and Brown- 
ing. The constants B, C, D, and E are from "Geographic tables 
and formulas" for the known latitude at Elk. Cosine a 7 and sine 
a? are functions of the azimuth Elk to Browning. The algebraic 
sign of each of these as fixed by trigonometric rules determines the 
sign of the resulting quantity. The signs of (II) and (III) are 
always positive; that for (IV) is always opposite to that of (I). The 
constant A / and secant <£' in the longitude computation are for the 
new latitude, which requires that the latitude computation be made 
first. These two factors will be the same for each of the pair of 
computations for the new position. For short lines, corrections 
(III) and (IV) will usually be less than o.oi" and may be neglected. 

When the logarithm of distance s in meters exceeds 4.0000000, a 
correction will usually be required for logarithm (V) for the differ- 
ence between the arc and sine. The constants for computing this 
are given on page 269, "Geographic tables and formulas," the argu- 
ments being log distance s and log (V). The difference between 
the values found from these is always to be subtracted from log 
(V) before finding its value in seconds. 

Six places of decimals will usually give sufficient accuracy for 

/A$\ 
log (VI). The logarithm of secant ( — ) may be taken from page 

268 of the tables. When log (V) is large, say over 3.5000000, a cor- 
rection in seconds will be needed for Aa expressed by the factor 
AA 3 F. The logarithm of (V) is multiplied by 3 and added to the 
logarithm of F, which is given in the tables; the value in seconds 
for the resulting logarithm is always to be added to the previously 
found value in seconds for (VI). 

The latitudes and longitudes for each point thus computed in 
pairs should agree within one or two hundredths of a second. The 
difference between the two reverse azimuths should also agree 
with the corresponding adjusted spherical angle within one or two 
hundredths of a second. 



36 INSTRUCTIONS TO TOPOGRAPHERS. 

The final step in the computation of triangulation is the tabula- 
tion of the results. A printed blank is used; on it is written the 
name of the station, the State and county in which it is situated, 
the kind of signal and the center mark used, a full description of 
the station (see p. 16), the latitude and longitude, the azimuth, 
back azimuth, and logarithm of distance in meters to all other sta- 
tions from which it is visible, also for each logarithm of distance the 
corresponding distance in miles and thousandths. 

Reduction of azimuth observations. 

Canada, Kentucky, triangulation station. June n, 2.30 a. m., 1910 (civil date). 
Latitude : 37 35' 46". Longitude : 82 21' 39". 

Watch time of observation 2 h 30™ 50 s a. m.= 14 11 3o m 50 s of the astro- H. m. s. 

nomic day which commenced at noon June 10 14 30 50 

Correction from seventy-fifth meridian time to 82 ° 21' 39" correction 

for 7 2i r 39" (p. in, "Geographic tables and formulas") —29 27 

Watch slow by telegraphic time -I- 23 

Local mean time (astronomic day) 14 01 46 

Correction, mean to sidereal time (p. 113, "Geographic tables and 

formulas," or p. 591, "Nautical almanac") +2 18 

Right ascension of mean sun at Greenwich noon, June 10, corrected 
for s h 29 111 27 s to change to noon at 82 21' 39" west longitude ("Nau- 
tical almanac," June, Table II; change for longitude made by Table 
III, last part of almanac) 5 12 45 

Sidereal time of observation 19 16 49 

Right ascension of Polaris for nearest Washington transit — June 10.8 
("Nautical almanac " circumpolar stars for June) 1 26 12 

Hour angle of Polaris at time of observation 17 50 37 

Hour angle of Polaris in arc=t (p. 112, "Geographic tables and form- 
ulas") 267 39' is'/ 

The daily change in Polaris is so slight that for the purpose of 
this computation no account need be taken of a fraction of a day 
in computing its position. 

The following are the formulas for azimuth and level correction: 

a sin t 
tan A= ~ I _5 cos 1 . a== sec cot &• <>— tan 4> cot d 

Level correction= — — [(w+w') — (e+e')] tan h\ 
4 



INSTRUCTIONS TO TOPOGRAPHERS. 37 

in which — 

0= latitude of station (37 35' 46"). 
A= azimuth of Polaris at time of observation. 
§= declination of Polaris at time of observation (88° 49' 21"). 
2=hour angle of Polaris at time of observation (267 39' 15") (both the sine 

and cosine of this angle are negative for this example). 
</=value of one division of level (2.0"). 
w t w'= readings of west end of level bubble, direct and reversed. 
e, e'= readings of east end of level bubble, direct and reversed. 

h= angular elevation of star (at elongation this is equal to the latitude, nearly). 

The following is the computation of the first of the preceding 
observations (page 20): 
2 

. Level correction^ — (2Xo.77)=o.77" 
4 
Log tan cf> 9. 88649 

Log cot d 8.31290 

Log cos t 8. 61205 (negative) . 

Log b cos t 6. 81144 (negative). 

b cos t — 1. 000648 

1 

1—6 cos t 1. 000648 

Log sec <f> o. 10109 

Log cot d 8.31290 

Log sin i 9. 99964 (negative). 

Log as'mt. . 8. 41363 (negative). 

Log 1—6 cos t. o. 00028 






Log tan A - 8. 41335 

A i° 29' oi." 7 

Level correction -f o. 8 

1 29 02. 5 

Add 180 to refer to the south =180 

Angle star to mark 64 18 32 



Azimuth of mark 245 ° 47' 34". 5 

Each azimuth computation should be made in a single column 
and for convenience the columns should be placed side by side in 
tabular form. 

GENERAL SUGGESTIONS TO COMPUTERS. 

Do not crowd your work; paper is cheap. 

Do your work in a systematic manner. If it permits tabular 
arrangement always use the forms approved by other computers 



38 INSTRUCTIONS TO TOPOGRAPHERS. 

unless you can convince them that yours are better. The Survey 
has printed forms for many purposes; these should be used whenever 
possible, for by their use the work is made more mechanical, and the 
more mechanically the work is done the less chance there is of error. 

A computer who is inexperienced or out of practice should check 
his work in every way possible. He should check logarithms either 
of numbers or of circular functions by using first a tabular value for 
a quantity less than the given one and then a greater tabular value, 
so that the differences in one case may be added and in the other 
subtracted. This operation may be reversed when the logarithm 
is given and numbers or angles are required. 

Errors are frequently made in taking out the first three figures of a 
logarithm from the wrong line where a dash over the fourth figure 
indicates that the first three should come from a lower line. 

As the algebraic signs of cosines and sines are so frequently re- 
quired, the rules governing them should be firmly fixed in the mind; 
as an aid to this remember the general rule that distances measured 
upward or to the right on the conventional plat of the quadrants of 
the circle are considered positive, others negative. The wrong use 
of signs is a very common source of error. 

Each step in a long computation, if it is not at once automatically 
checked, should be checked by repeating the computation. 

Check the copying of angles, distances, etc., taken from adjusted 
results for use in new computations; also check figures carried from 
page to page. 

Gross errors are sometimes made by using the sine when a cosine 
is required, or by writing a product in the wrong column, as east for 
west in primary traverse computations. 

Placing the decimal point in the wrong place is a common mistake. 
This may in many cases be corrected by a mere inspection of the 
quantity to see whether it appears of proper value. 

Good judgment should be exercised in the degree of accuracy 
sought for a given result. For the preliminary computation of 
geodetic positions, for example, six-place logarithms will probably 
suffice; these can be taken from a seven-place table with only a 
rough interpolation. A four-place logarithm can often be used to 
advantage. The accuracy of the results obtained should equal the 
requirements; more than this involves a waste of time. 






INSTRUCTIONS TO TOPOGRAPHERS. 39 

For convenience the foot, yard, and mile are the units adopted for 
all Geological Survey field work, but for geodetic computations meters 
are used. The best conversion tables for metric and English measures 
are those published by the Bureau of Standards, edition of 1910. 
In using these all changes from one system to another should be 
checked by reversing the operation. The logarithms for the inter- 
change of these measures are given on page 301 of "Geographic 
tables and formulas." 

PRIMARY TRAVERSE. 

FIELD WORK. 

Personnel of party. — In primary traverse the party consists of an 
instrument man in charge, a recorder, two tape men, and two flagmen; 
also a cook and a teamster when camping is necessary. 

Instruments, notebooks, etc. — The following supplies can be ob- 
tained on requisition : 

One transit, graduated to 20 or 30 seconds, and furnished with stadia wires. 

Two 300-foot steel tapes, graduated to feet throughout. 

One 100-foot steel tape. 

Two red and white transit rods. 

Two plumb bobs. 

Eleven tally pins. 

Four hand recorders. 

Two electric hand lamps. 

One tape repair outfit, punch, and rivets. 

Three tape clips, temporary repairs. 

Two tape holders. 

One set steel dies, figures. 

One set steel dies, letters. 

Three large book bags. 

Standard bench-mark tablets or posts (according to the requirements of the 

country) . 
Canteens. 
Cement (in cans). 

Drills, hatchet, hammer, post-hole digger. 
Primary traverse field notebooks 9-928. 
Tape men's notebooks 9-929. 
Blank notebooks 9-896. 
Book of instructions. 

The instrument man must carry a reliable watch. 



40 INSTRUCTIONS TO TOPOGRAPHERS. 

Location of line. — Primary traverses should always be run in cir- 
cuits or tied to points previously located. In 1 5-minute quadrangles, 
in country where routes can be readily planned, traverse lines should 
follow as closely as possible the borders of the quadrangles to be con- 
trolled, not departing from them more than is absolutely necessary 
to keep on roads. If there is a choice of roads select the one in 
unmapped areas. An additional line should be run to bisect the 
quadrangle. 

In areas where the country will not permit this plan to be followed 
economically and where the selection of routes for the lines must be 
influenced by the location of highways, it will be necessary to plan 
the routes to meet the specific requirements. 

Permanent marks. — In regions where topographic conditions per- 
mit, tablets or iron posts (see C and F, PL I) must be set as near as 
possible to each corner of each 1 5-minute quadrangle, one on each 
side halfway between the corners and one in the center, making nine 
in all. All such marks must be stations on the line and should be 
stamped "Prim. Trav. Sta. No. — " (and numbered consecutively) 
and also with the year of survey. In areas which can not be trav- 
ersed according to the regular plan, permanent marks must be 
established at intervals not greater than 6 miles. 

In cooperating States use the appropriate State post or tablet (A , 
PL I). 

Where level bench marks have been established along the route of 
survey, they should be tied to and stamped as above and thus made 
to serve as permanent marks on the traverse line. 

It is desirable that every permanent point be tied to two or more 
witness or reference points, the bearings, distances, and descriptions 
being duly recorded in the notebook. 

Secondary points. — Besides the permanently marked points, a 
number of other points should be carefully located along the traverse, 
and these points should be specifically designated in the field notes. 
Of special importance are the crossings of boundaries of States, 
counties, and civil townships, and the locations of the principal 
cross roads, of railroad stations when the line follows a railroad, and 
of township and section corners if the region is subdivided by public- 
land surveys . Note should also be made of less important landmarks, 



INSTRUCTIONS TO TOPOGRAPHERS. 4 1 

such as road forks, mileposts, railroad switches, road and stream 
crossings. These points should be so completely described in the 
notebook as to be readily identified. 

Duties of tape men. — The front tape man carefully marks off each 
tape length; if on a wagon road, with tally pins; if on a railroad, with 
keel on the rail. Bach time he marks off a tape length he registers 
it on his hand recorder; each time the rear tape man reaches the mark 
left by the front tape man he does likewise. When a transit station 
is established the two tape men compare their hand recorders for 
check on tape length. Should they differ, the course must be re- 
measured. 

Transit stations should be made at even tape lengths or even 
io-foot marks, wherever possible, in order to simplify the work of 
the computer. They should be selected at points affording not 
only an unobstructed view back to the transit but also a clear view 
forward. Each station is to be marked, if on a wagon road, by a 
io-penny nail driven into the ground and through a piece of paper 
on which the front tape man has written the number of station and 
distances; if on a railroad, by a keel cross on rail, with number and 
distance on nearest tie. 

Stations on main lines are to be numbered consecutively, begin- 
ning with zero; those on short spur lines to section corners or other 
points to be computed are to be lettered instead of numbered. Sta- 
tion numbers should never be duplicated in a single locality. 

The two tape men must keep in book 9-929 separate records of the 
number of stations and distances between them. At noon and at 
night these records must be compared with the recorder's notes, and 
should there be a difference, it must be corrected before the line is 
carried forward, the line being retraversed if necessary. 

In locating transit stations the front tape man should bear in mind 
that it is desirable for the instrument man to be able to sight the 
bottom of the rod in each direction. This is especially important 
on short sights, for errors due to sighting the upper part of a rod which 
may be out of plumb may appreciably affect the accuracy of the line. 

Method of measuring. — When measuring along a wagon road the 
tape must be kept horizontal unless the grade is very slight; on 



42 INSTRUCTIONS TO TOPOGRAPHERS. 

steep slopes a plumb bob must be used either to bring the tape end 
vertically over an established point or to establish a new one, as the 
case may be. Judgment should be used in selecting the proper 
length of tape on slopes. No attempt should be made to use the 
full 300-foot length; about 150 feet is ordinarily all that a tape man 
can hold horizontal with the proper tension and plumb at the same 
time. On slopes that require "breaking" the tape into short sec- 
tions, the entire tape should first be drawn forward its full length 
by the front rodman if convenient, or by the front tape man, who 
then returns to help "break" the tape at the proper places, until 
the end of the tape is reached. In this manner the distance is meas- 
ured on the whole tape and does not depend on the sum of the 
separate horizontal measurements. 

Some tension must be put on the tape, but the use of a spring 
balance has been found by experience to be unnecessary. 

Errors in taping. — The errors that most seriously affect the accu- 
racy of taped lines may be classed under two heads. 

The errors of one class are due to failure to keep the tape 
horizontal and to careless plumbing. The instrument man should 
impress tape men with the fact that the accuracy of traverses depends 
on their correct taping more than on the instrument work, for the 
latter is checked at every azimuth observation, whereas there is no 
check on the taping until the circuit is closed. 

The errors of the second class are gross mistakes arising generally 
from carelessness in counting tape lengths. They may be eliminated 
by checking the count of tape lengths by independent measurements. 
To do this, the instrument man should read each distance by stadia 
on the red and white transit rod or on a special stadia rod carried 
for this purpose. In case the distance is too great to be read by a 
single sight, he should set up the transit between stations and read 
both front and rear rods. Stations should in no case be more than 
2,600 feet apart, which is about the limit of visibility of the rod. 
On railroads an additional check on the taping may be had by count- 
ing rail lengths. This should be done by both rodmen and by the 
recorder, or by the instrument man while moving from one station 
to the next. In other places a check may be had by pacing. 



INSTRUCTIONS TO TOPOGRAPHERS. 43 

Method of reading deflection angles. — At each station the instrument 
man should proceed as follows: Sight rear flag with transit circle 
set at last reading at previous station, transit telescope, sight front 
flag, and read both verniers. Turn instrument with the two plates 
clamped, the vernier remaining undisturbed; sight rear flag again 
and remeasure the angle. If the two results thus obtained differ 
more than 60", repeat the operation. 

When the transit is carried from one station to the next, keep the 
upper plates clamped so as to retain the last vernier reading; after 
setting up the instrument verify the reading and use it as the first 
back sight reading at the new station. It may at times be necessary, 
in order to get the best pointing on the rod, to change the reading a 
minute or two, but by following this general plan a useful check on 
the readings is secured without trouble. 

Azimuth observations. — Observations on Polaris for azimuth must 
be made at the close of each day's work, if the weather permits. On 
a crooked line with many short courses azimuth stations should be 
not more than 100 stations apart; on a traverse with long tangents 
they should fall not more than 15 miles apart. These requirements 
may necessitate going back over the line in order to make the neces- 
sary observations, but if conditions are favorable it is possible to make 
azimuth observations in broad daylight. 

Both the transit and the azimuth mark must be at stations in the 
traverse not less than 500 nor more than 1,500 feet apart. Each 
point should be marked by a stake with a tack, or, if, on a railroad, 
by a nail in a tie. The azimuth mark may consist of a vertical slit 
one-eighth inch wide and 6 inches long cut in the side of a box or tin 
can containing a candle or lantern, which should be carefully cen- 
tered over the tack in the stake. In pointing the telescope use the 
electric hand lamp to illuminate the cross wires, holding it nearly 
in front of the object glass. 

Angles should be read as follows: Set on azimuth mark, then on 
star; reverse telescope, set on star again, and then on azimuth mark. 
Bach observation should consist of not less than three direct and 
three reversed measurements, the circle being shifted for each set 
by about 60 °. (See sample page of record, p. 44. ) Observations may 



44 



INSTRUCTIONS TO TOPOGRAPHERS. 



be made at any time the star is visible, but preferably when at or 
near elongation. The time of setting the cross wires on the star must 
be recorded to the nearest second. Observations should be made 
rapidly; not more than 10 minutes need be taken to complete a set. 
The notes must be kept in the following form : 

Date, Sept. 10, 1910. Line from Pikeville west to Dayton, Mo. 

Azimuth observation 2.5 miles southeast of Dayton, Mo., Sept. 10, 1910. Mag. dec. 
sta. 326-327 N. 57 30' W. Lat. 39 00'. Long. 92 ° 15'. 

Instrument at station 326. Mark at station 327. Watch 35 seconds fast, ninetieth 
meridian time. 



Point. 


Vernier A. 


Vernier B. 


Mean. 


Deflection 
angle. 


Azi- 
muth. 


Time. 


Mark 


1 a 

216 54 00 

274 48 00 

94 SO 30 
36 56 00 

348 02 30 

45 57 00 

225 57 00 

168 02 00 

95 05 00 
153 01 30 
333 02 30 

275 06 30 


1 11 

36 54 00 

94 48 00 

274 50 30 
216 56 00 

168 02 00 

225 56 30 

45 57 00 

348 02 30 

275 06 00 
333 01 00 
153 03 00 

95 06 00 


1 n 

36 54 00 
94 48 00 

94 50 3° 
36 56 00 

168 02 15 
225 56 45 
225 57 00 
168 02 15 

95 05 30 
153 01 15 
153 02 45 

95 06 15 


/ // 

57 54 00 
57 54 30 

57 54 30 
57 54 45 

57 55 45 
57 56 30 


/ // 


H. m. s. 


Star a 


8 31 33 
8 34 48 


Star 


Mark 


Mark 




Star « 


8 40 28 
8 41 50 


Star 

Mark 


Mark 




Stara 


8 43 55 
8 44 56 


Star 


Mark 








57 55 00 
Watch fast 


8 39 35 
35 




Corrected t 


ime 


8 39 00 



a Reverse telescope between each two readings on star. 

The latitude and longitude of each azimuth station, scaled from 
the best map available to the nearest minute, should be given, 
together with the date of observation, on the page with the other 
records, in order to enable the computer readily to convert standard 
to local mean time. 

In case unfavorable weather prevents the taking of the azimuth, 
leave adequate marks at a point selected, before proceeding with 
the line, and return to them later to make the observations. 



INSTRUCTIONS TO TOPOGRAPHERS. 45 

Watch error. — The instrument man must carry a reliable watch and 
keep it in good condition. He should ascertain its error daily by 
comparison with telegraphic time, which is sent over Western Union 
lines once a day. In case he has no opportunity to make this com- 
parison while running the line, he should do so as often as possible, 
figure the rate of error per day, and record the proper correction for 
each azimuth observation made. A watch error of 20 seconds or less 
will not appreciably affect the accuracy of the determination. At 
least once in each notebook he should state whether he uses standard 
time; if so, for what meridian. 

Magnetic declination. — A careful reading of the needle for magnetic 
declination should be made at frequent intervals and recorded 
opposite the proper station number in the notebook. Such deter- 
minations should be made at each azimuth station and at favorable 
points along the line where the needle is not likely to be affected by 
rails, electric wires, or similar disturbing elements. At azimuth 
stations determine the magnetic bearing of the azimuth mark at the 
time it is established. If the line follows a railroad, magnetic 
determinations should be obtained from a parallel line at a distance 
of 25 yards from the rails or wires. 

Field record. — Complete notes must be kept by the recorder in 
book 9-928, to be written in a plain, neat hand with a No. 4 pencil. 
The blanks in the title-page should be filled in the first day the book 
is used. A single line should be drawn through erroneous records, 
which must never be erased. 

The recorder must take down the vernier readings, as they are called 
off by the transit man, and compute the mean pointings and deflec- 
tion angles, giving proper signs to the latter. He must keep up with 
the instrument man in these computations, as they enable him to 
note by inspection whether the instrument man has made errors in 
his readings and to call attention to them before the instrument is 
removed from the station. He should take special pains to see that 
the degree and minute numbers for the two verniers are consistent 
and are recorded in the proper column. 



46 INSTRUCTIONS TO TOPOGRAPHERS. 

The notes are to be kept in the following form : 
Date, Sept. 9, 1910. Iyine from Pikeville to Dayton, Mo. 



Stations, dis- 
tance between. 


Vernier 
A. 


Vernier 
B. 


Mean. 


Deflec- 
tion 
angle. 


Azimuth. 


Remarks. 


Sta.326:3tapes, 
900 feet. 


/ // 

[316 51 30 
<275 06 00 
(.233 21 00 

[233 21 30 
<279 04 30 
I324 48 30 

, stream crc 
t, crossroad 

[324 48 30 
{342 08 00 

1359 27 00 


/ // 

136 52 30 
95 07 30 
53 22 00 

53 22 00 

99 05 30 

144 49 30 

»ssing. 
at Tanbarl 
144 49 30 
162 09 00 
179 28 00 


/ 

316 52 
275 06 
233 21 

233 21 

279 05 
324 49 

:P.O. 

324 49 
342 08 
359 27 


11 

00 
45 
30 

45 
00 
00 

00 
30 
30 


/ // 

41 45 15 
4i 45 15 


t a 
«I23 35 00 


Sta. 326-327; 

N. 5 7°3o'W. 
Stadia 905. 




5 81 49 45 
c 81 49 47 


Sta. 327: 4 tapes 
+ 120 — 1,320 


-4i 45 15 

45 43 15 
45 44 00 


Stadia 1,330. 


feet. 

Sta. 327+90 feet 
Sta. 32 7+430 fee 

Sta.328:26ofeet. 


&I27 33 22 
<*I27 33 26 


+45 43 37 

17 19 30 
17 19 00 


Stadia 250. 




+ 17 19 15 


6144 52 37 
C144 52 43 



o Written in red ink. & Written with black pencil. c Written with black ink. 
Note. — The entries in the azimuth column are a part of the office computation. 

The record must contain also a description of the starting and 
ending points of the line, of each permanent mark established along 
the line, of each point which is to be computed for the use of the 
topographer, and of all crossings and other landmarks that may be 
of value to him. Such descriptions should be concise, yet full 
enough to leave no possible doubt as to the identity of the points 
described. Each should be supplemented by an explanatory sketch 
if necessary. 

Example of description of permanent mark : 

Station 1025, bench-mark tablet stamped "Prim. Trav. Sta. No. 4, 1910," set in 
sandstone ledge, top of Walden Ridge, 3 miles northwest of Dayton, Tenn., at junc- 
tion of Dayton, Pikeville, and Morgan Springs Roads, 325 feet west of residence of 
John Neilson. Reference marks: Cross cut in ledge 60.25 f eet N. 25 30' E.; spike in 
root of white oak tree 14 inches in diameter, 75.60 feet N. 45° 15' W. 



INSTRUCTIONS TO TOPOGRAPHERS. 47 

Examples of description of points to be computed and other 
landmarks : 

Station 625+730 feet [center of crossroads at Antioch Church]. 
Station 720+320 feet, east abutment of bridge over Glade Creek. 

Station 73 2 H feet, road fork at Johnson blacksmith shop. 

Station 926+210 feet Ccenter.of track opposite semaphore, Lee station]. 

Station 936+300 feet, road crossing one-half mile east of Sequatchie railroad bridge. 

Each point to be computed should be marked with brackets in 
ink immediately upon its selection by the instrument man. 

COMPUTATIONS. 

The steps in primary traverse computations are as follows : 

1. Computation of azimuths. 

2. Computation of azimuths of each line from the observed deflection angle. 

3. Adjustment of closing errors of azimuth. 

4. Computation and tabulation of latitudes and departures, which are the 

north and south distances and the east and west distances, by two com- 
puters working independently. 

5. Latitude and longitude computation. 

6. Adjustment of closures in positions. 

7. Tabulation of results by atlas sheets. 

The computations for 1, 2, and 3 are made in the original field 
record book, 9-928; those for 4, 5, and 6 are in book 9-931. The 
abstracts of results (7) are placed on long sheets of blank paper. 

Reduction of observations on Polaris for azimuth. — First find the 
mean of time of observations and corresponding mean of angles 
measured between mark and star (p. 44). Having ascertained the 
approximate latitude and longitude of the azimuth station, compute 
the true azimuth of star by tables given on pages 14 to 25, inclusive, 
''Geographic tables and formulas." 1 For any hour angle or lati- 
tude not given in Table 3, pages 20 and 21, the azimuth to 0.1 min- 
ute can usually be mentally interpolated. 

1 Commencing with the year 191 1 the General Land Office will issue yearly tables of 
azimuths of Polaris giving declination, elongation, and culminations for each day in 
the year. These tables should be used whenever available in preference to those in 
"Geographic tables and formulas." Be sure to note whether tabular culminations 
are for a. m. or p. m. 



48 INSTRUCTIONS TO TOPOGRAPHERS. 

Example of computation: The station is in latitude 39 ° oo' N., 
longitude 92 ° 15' W. 

H. m. s. 

Sept. 10, 1910, ninetieth meridian standard time of observation 8 39 00 

Correction for 2 ° 15' longitude — 9 00 

Local mean time of observation $ 30 00 

Add 24 hours, thus finding the interval from noon Sept. 9, because Table 1 

for September gives upper culmination at an hour greater than 8 h 30 m . 24 00 00 

32 30 00 

Upper culmination (Table 1), Sept. 1 , 14 41. 9 

Correction to reduce to year 1910 (Table iA) +3.0 

Correction (Table iB) for 9 days —31- 5 

Upper culmination, Sept. 9, 1910 14 13. 4 

Time of observation 32 30 

Hour angle 18 16.6 

This hour angle, being greater than n h s8 m , indicates that the star was east 
of north. In order to enter Table 3 this hour angle must be subtracted 
from 23 11 56™. 1 23 56. 1 

Time argument for Table 3 5 39. 5 

For which the azimuth found by a double interpolation is 90', 
east of north. 

To which 180 is to be added to refer to south. 

To interpolate for hour angles near elongation, use for the latter 
5 h 55 m an d take the corresponding angle from the line next below 
the five-hour time given (or the line next above if more than six 
hours), which is the yearly mean elongation angle; or, more accu- 
rately, take the elongation angle from Table 2 corrected for the month . 
When using Table 3, 0.5 should be added wherever a period is 
given after the figures for minutes. 

o in 

Azimuth of star (90' east of north) 181 30 00 

Angle between mark and star (p. 44) (star east of mark) 57 55 00 

Azimuth at station 326 to 327 1 123 35 00 

A rough check on this azimuth is found by comparison with the 
observed magnetic bearing, allowance being made for declination. 
Each azimuth computation is to be made in the field notebook on 
the same page with the observation. 

This azimuth is written in red ink in the azimuth column of field 
notebook (see example on p. 46) on the line with the station number. 



INSTRUCTIONS TO TOPOGRAPHERS. 



49 



The deflection angle is added or subtracted according to its sign, and 
the sum or remainder is written in pencil on the line with the mean 
deflection angle. The next deflection angle is combined according 
to its sign with this azimuth and the result placed in pencil opposite 
the deflection angle used. This process is repeated until the next 
computed azimuth written in red ink is reached. The last azimuth 
in pencil will probably not agree with the observed azimuth. For 
any line not running due north or south there will be a discrepancy 
between observed and computed azimuths, due solely to convergence 
of meridians, which for latitude 30 will be 0.5' for each mile run 
east or west; for latitude 49 ° the amount will be i / . If no large 
errors appear in the results, the discrepancy between computed and 
observed azimuths at the second station is to be divided by the 
number of stations and a proportional correction applied to each 
penciled azimuth, the corrected figures being written in black ink. 
Latitudes and departures are to be computed in book 9-931 ss 
shown below: 

Line from Pikeville to Dayton, Mo. 



Station. 


Azimuth. 


! 


Cosine. 


North. 


South. 


East. 


West. 


326—327 

327+430 


t n 

81 49 47 
127 33 26 

127 33 26 


900 
430 


0. 990 
•793 


0. 142 
. 609 


262 


128 




891 
341 








8QO . ^OT. 


. 609 


262 

128 


128 




I>2 3 2 


327+430 — 328 . . . 


134 
542 


706 















Natural sines and cosines for the azimuth given are written in the 
proper columns. By means of Crelle 's tables the products of these by 
distances are found and placed in the proper columns. The sines 
multiplied by the distance give departures east or west; when the 
sine is positive the new point is west, when negative it is east. 
Cosines multiplied by distances give latitudes north or south; when 
the cosine is negative the new point is north, when positive it is 
south. The direction of the new point can readily be determined by 
8221 — n — 4 



50 INSTRUCTIONS TO TOPOGRAPHERS. 

noting the azimuth, remembering that o° azimuth is for a line run- 
ning due south, qo° for a line due west, 180 for a line north, and 270 
for a line east; in the example 81 ° 49' 47", being for an azimuth 
between due south and due west, will be to a point southwest. For 
long distances four decimal places in sines and cosines should be 
used. Whenever a point is reached for which the latitude and 
longitude are desired, as at 327 + 430 in the example, leave six blank 
spaces for the computation. The data for the computation for such 
a point are found from the record on page 46, as follows: For the 
crossroad at Tanbark post office, which is on line between stations 
327 and 328, the azimuth is the same as to station 328. The distance 
by measurement is that given, 430 feet from station 327. In order 
to make the computations continuous, station 328 is taken as 1,320— 
430=890 feet from the intermediate point used, the azimuth being 
the same for both points. 

The next step in this work is the computation of latitudes and 
longitudes. These should be determined for important points a 
mile or less apart. Assume, for illustration, that for station 326 
(p. 46) the coordinates have been computed, and that 3274-430 is the 
next location desired; each of the four columns, north, south, east, 
and west, is summed and the difference between the sums of the north 
and south columns is placed in the column of the greater; likewise, 
the difference between the east and west columns is placed in the 
column of the greater. The computations of latitude and longitude 
and the descriptions of the points are placed on the right-hand page 
of the book opposite the group of stations. 

The logarithms of the geodetic constants for metric measures, called 
1 'the A, B, C factors," are on pages 196 to 267, inclusive, of "Geo- 
graphic tables and formulas." Factors A and B are used to five 
decimal places only; these will be practically constant for a distance 
of 10 or 15 miles north and south, the value for the middle latitude 
being used. 

For the example on page 49 : 

Log distance 134 (north) 2. 12710 

Log to reduce feet to meters 9. 48402 

Log B for latitude 39 00' 00" 8. 51093 

. 12205 



INSTRUCTIONS TO TOPOGRAPHERS. 51 

The sum, 0.12205, is the logarithm of change in latitude in seconds 
between station 326, and 326+430=1. 32" (north). 
For change in longitude: 

Log distance 1,232 (west) 3.09061 

Log to reduce feet to meters 9. 48402 

Log A for latitude 39 00' . 8. 50914 

Log secant of middle latitude 10950 

Log of change in longitude in seconds 1. 19327 

New point west 15-61" 

These differences are to be added to the latitude and longitude of 
station 326. 

In order to check the plotting the distance between successive 
positions must be computed, as the lines are seldom as much as a mile 
in length and never over 2 miles, the latitude and departure can with 
sufficient accuracy be taken as the base and perpendicular of a plane 
triangle. The distance sought will then be the hypothenuse and its 
square will be equal to the sum of the squares of the base and altitude. 
For distances less than 10,000 feet Barlow's tables should be used in 
finding squares or square roots. The distance should be written in 
red ink, inclosed in a circle, on the right-hand page of the computa- 
tion book in the blank space between the two stations referred to. 
After the record is complete its accuracy should be tested by com- 
puting a side from the given distance (hypothenuse) and the other 
side. 

These operations are repeated for each selected point until the 
traverse line closes back on itself or ties to another point previously 
determined. The errors of closure for a 15' quadrangle, if not in 
excess of i 7/ in latitude or 1%" in longitude, may be distributed 
proportionately between initial and closing points. 

Where so many operations are involved errors are very likely to 
creep into the computations. Therefore each step of the work 
should be checked as well as possible. The azimuth computation 
should be compared with the observed magnetic bearings, but 
because of the possibility of local variation little dependence can 
be placed on this comparison as a check. If the computed and 
observed azimuths for a line differ about io', look for an error of 
that amount in the deflection angle or in the adding and subtracting 



52 INSTRUCTIONS TO TOPOGRAPHERS. 

of deflection angles to azimuths. If the difference is larger it is 
very likely that a wrong sign has been used for a deflection angle. 
To find the error, divide the difference by 2 and look for a deflection 
angle with an incorrect sign equal to the quotient. Errors of about 
180 occasionally result from the recorder placing the vernier readings 
in the wrong columns. By a careful inspection of the records it is 
sometimes possible to detect such an error. The latitudes and 
departures should be computed by two persons working independ- 
ently of each other; after each has completed his work the results 
should be compared and differences corrected and verified. Errors 
are often made in multiplication by the distance, the decimal point 
being in the wrong place, or the product is written in the wrong 
columns — in the north column when it should be in the south 
column, etc. 

VERTICAL CONTROL. 

PRIMARY AND PRECISE LEVELING. 

GENERAL INSTRUCTIONS. 

Distribution of primary-level control. — A sufficient amount of 
accurate spirit leveling should be done to insure the placing of at 
least two standard bench marks in each township or equivalent 
area surveyed, except in forest-clad or mountain areas, where at 
least one such mark should be placed in each township. 

Permanent bench marks should be established along level lines at 
intervals of approximately 3 miles, unless otherwise instructed, and in 
no case should the distance between bench marks exceed 6 miles. 

Location of permanent bench marks. — Bench marks should be estab- 
lished, if practicable, at the township corners of the public-land 
surveys, near all important lakes and reservoirs, at the crossings 
of important streams and divides, in every city or town passed 
through, and in the vicinity of important mines. They should be 
so located as not to be liable to injury or disturbance, yet should 
be so prominently situated that they can easily be found. Along 
a railroad or highway bench-mark posts if used should be placed 
either outside of and close to the right of way or on the right-of-way 
line. They must not be set close to trees, telegraph poles, or fence 
posts. 



INSTRUCTIONS TO TOPOGRAPHERS. 53 

Character, setting, and marking of permanent bench marks. — Standard 
bench marks consist either of tablets fastened with cement into solid 
rock in place or into masonry structures, such as the foundations of 
buildings or bridge piers, or of iron posts set in the ground so as to 
project not more than i foot and surrounded by a conical mound 
of earth about 3 feet in diameter raised to half the height of the 
post. 

Portland cement in air-tight cans is furnished from the Washington 
office for use in setting tablets. If good clean sand is available it 
can be mixed with the dry cement in equal parts. The drill hole 
for the tablet must be well cleaned and wet. The cement and 
sand, or cement alone if pure sand can not be conveniently procured, 
should then be thoroughly mixed with water to a thick paste, and 
the drill hole filled with it; into this the tablet should be pressed, 
the excess cement being forced out so as to completely fill the space 
under the tablet face. In order that the cement may set well it 
should be kept damp and protected from the sun for at least a day, 
and it must not be allowed to freeze for 12 hours. Dry earth or a 
piece of sacking will probably be sufficient protection. When a 
tablet is set in a vertical wall it may be necessary to hold it in place 
by a prop of some kind for a few hours. 

The intersection of the cross lines on either style of mark is the 
reference point. Before a tablet is set the figures indicating the 
elevation (to the nearest foot only) are to be stamped into the metal 
before the word "feet." 

In cooperating States the name of the State must be stamped or 
cast on standard bench marks. 

If a tablet is inconspicuously situated, a mound of rock should be 
erected near it, the rock about it be marked with paint, or a near-by 
tree blazed as a witness tree. 

The steel tape can often be used to advantage instead of the 
leveling rod for determining the elevation of a tablet set in a vertical 
wall. 

All standard bench marks should be used as turning points in the 
line, but where this can not be done, their elevation must be deter- 
mined by two readings from different set-ups, or from separate tempo- 
rary bench marks. 



54 INSTRUCTIONS TO TOPOGRAPHERS. 

Temporary bench marks. — Temporary bench marks should be set at 
intervals ranging from half a mile to i% miles. They may consist of 
chiseled marks on solid rock or masonry, or copper nails with washers, 
or spikes, driven in telegraph poles, mileposts, fence posts, or trees. 
The copper nails with lettered washers must be used when prac- 
ticable. Where there are no natural objects for temporary bench 
marks, pieces of iron pipe, about 20 inches long, may be used. 
Select a place where the mark will not be likely to be disturbed and 
yet can be readily found, preferably near a road junction, so it will 
afford a convenient tie point for other levels or traverses. The 
location should be conspicuously indicated by large figures in white 

or red paint, thus: 

u s 

[elevation] 
B M 

Useful elevations. — Besides the bench marks above described a 
number of intermediate elevations are required for the use of the 
topographer, and these also should be selected with a special view 
to their usefulness in topographic mapping. The levelman should 
bear in mind that his work is not an end in itself but a preparation 
for the work of others, and that the accuracy with which his circuits 
check, though of paramount importance, is not the only thing that 
determines its utility. 

Ground elevation should be painted conspicuously along the side 
of the road, on fences, telephone poles, trees, or rocks. If prac- 
ticable, they should all be marked on the same side of the road, 
preferably on the north or east side. 

The points at which elevations are particularly desired are the top 
of the rail at railroad stations, junctions, sidings, and crossings, the 
ground at crossroads, road forks, and bends; on summits and ridges; 
near schoolhouses and other public buildings, lone houses, and 
important mines, quarries, and oil, gas, and artesian wells; on some 
permanent part of a bridge other than a wooden floor; the water 
surface of streams under bridges, at stream crossings, and above and 
below dams; and water surfaces on lakes and reservoirs. Where 
water-surface elevations are recorded, always give the date. 

The number of these elevations should be varied with the nature 
of the country and the contour interval; thus in rugged regions 



INSTRUCTIONS TO TOPOGRAPHERS. 55 

mapped with 50-foot or 1 op-foot intervals relatively few elevations 
are required (mostly on summits and in hollows); but in areas of 
gently rolling relief they should be more numerous. In flat areas 
where 5 or 10 foot contours are used, each contour crossing should be 
marked with a stake or otherwise. This is important, as in such 
areas a difference in elevation of a few tenths of a foot may mean a 
difference of several hundred feet in the location of a contour. 

Descriptions of bench marks and useful elevations. — Complete 
descriptions of all bench marks and useful elevations must be made 
in the notebook and copied in the description book (9-916) at the 
close of each day's work. A sketch must accompany the description 
of each standard bench mark, showing directions and distances to 
near-by objects. 

Descriptions should be written with items in the following order: 

1. Name of the nearest post office, town, village, or other well- 
known locality, with direction and distance from it to the bench 
mark in miles and tenths; or township, range, and section in which 
bench mark stands, with direction and distance from nearest corner. 

2. Position with reference to buildings, bridges, mileposts, street 
or road corners. 

(Items 2 and 3 should be written in direct form of speech.) 

3. Description of object on which the bench mark is placed — tree, 
bowlder, bridge, etc. 

(The above three items answer the question where and should be 
followed by a semicolon (;) and by item 4, which answers the ques- 
tion what.) 

4. Nature of the bench mark — copper nail with washer, bolt, mark 
on rock, tablet, post, etc. — and how marked or stamped. Old bench 
marks must be fully described. 

Descriptions should be kept in the order in which the bench marks 
occur. If standard bench marks are not established when the line 
is first run, spaces should be reserved in description books for them 
in their proper order. A brief description of the line should be given 
at frequent intervals, especially when changing direction. When 
circuits are closed, complete descriptions of closing points, closure 
error, old and new elevations, and page reference to connecting 
points should be given. A plot of all lines or circuits must be made 



56 INSTRUCTIONS TO TOPOGRAPHERS. 

on a page near the back of the description book for each group of 
circuits and the names of enough places to identify the line readily 
should be added. Boundaries of quadrangles should be shown, and 
also, if the area is covered by public-land surveys, the position of 
the line with reference to township and section lines. Alongside of 
each line reference to the page of the description book where the 
record is made should be entered. The records in this book are 
incomplete without this diagram. 

PRIMARY LEVELING WITH Y LEVEL. 

Personnel. — A primary level party consists of a levelman, one or 
two rodmen, and in some cases a bubble tender. 

Instruments, notebooks, etc. — The instruments required are as 
follows : 

One 20-inch Y level. 

One or two New York rods. 

One or two plumbing levels. 

Two steel turning pins. 

One set dies (figures and letters). 

One 25-foot steel tape. 

Bench-mark tablets or posts. 

Copper nails and washers for temporary bench marks. 

Cement in cans. 

Level notebooks 9-903 (those in black covers to be used by levelmen; those in 

yellow covers by rodmen). 
Bench-mark description book 9-916. 
Two book bags. 

Other accessories to be purchased in the field: 

One or two hatchets. 
One drill hammer. 
One posthole digger. 
Stone drills (iMi-inch bit). 

Character of lines. — Primary levels should be run as single lines in 
circuits wherever practicable, otherwise checked by rerunning, 
preferably in the opposite direction. No work is completed until 
it is checked in some way. Lines should be connected with near-by 
bench marks of railroads, cities, and other organizations. 



INSTRUCTIONS TO TOPOGRAPHERS. 57 

Accuracy. — The allowable closure error of a circuit in feet must 
not exceed 

0.05 -y/ length of circuit in miles. 

If it is greater than this, the facts must be reported to the geographer 
in charge immediately. 

Adjustment of instruments. — The adjustment of the level must be 
tested daily and corrected whenever it is found in error; the adjust- 
ments of the line of collimation and of the level tube are especially 
important. 

The tripod clamping screws must be loosened before the instru- 
ment is set and tightened after the legs are firmly placed. After 
setting the target and before the "all right" signal is given the level 
bubble should be examined, and if found to be away from center 
it must be corrected and the target reset. 

Equalization of fore and back sights. — In order to eliminate instru- 
mental errors and errors caused by curvature and refraction, it is 
very important that the length of fore and back sights be equalized, 
but when this is impracticable as soon as the obstacle is passed 
enough unequal sights to balance should be taken, provided this can 
be done before a readjustment of the level is made. When the 
adjustment of the level is changed, further attempts to eliminate 
instrumental errors by the balancing of previous sights are useless. 
The failure to balance sights is one of the principal sources of error. 

Maximum length of sight. — The maximum length of sight permissi- 
ble under the most favorable conditions is 300 feet, except when cross- 
ing rivers or deep ravines. In such places proceed thus: Establish 
a turning point on each side; set up the level about 20 feet from each 
point in turn, taking in the first position a back sight to the near 
point and a fore sight to the distant point; then cross the stream or 
valley and take a back sight to the distant point and a fore sight to 
the near point. For very long sights several readings should be 
made on the distant rod and the mean adopted. The mean of these 
determinations of elevation may be accepted as the true one. 

Measuring of distances. — Distances may be measured by stadia 
readings on the rod, by counting rails if along a railroad, or by pacing. 
The distances in miles of both fore and back sights must be recorded 
in notebooks in the proper columns. 



58 INSTRUCTIONS TO TOPOGRAPHERS. 

Unfavorable conditions. — Work on primary lines should not be 
carried on during high winds or when the air is boiling badly. During 
very hot weather an effort should be made to go to work early and 
remain out late, rather than to work during midday. 

Inspection of rod. — When the rod is lengthened beyond 6.5 feet, 
both the rodman and the levelman must examine the setting of the 
target as well as the reading of the rod vernier. When the rod is 
closed they should see that the rod vernier indicates 6.5 feet, not 
depending on the abutting ends to bring it back to place. The lower 
end of the rod and the top of the turning point must be kept free 
from mud and dirt. 

Plumbing levels must be tested at intervals and kept in adjust- 
ment. 

Turning points. — The regular steel turning-point pin should be 
used wherever no rock or other suitable points are available. A 
marked point on the top of the rail may be used when running along 
railroads. 

Reading of target. — Both the levelman and the rodman must read 
each target setting independently and keep separate records. They 
should not compare figures until their respective records for a given 
sight are completed. If the difference exceeds 0.001 foot,, each 
must read the rod again before comparing anything but results. 

Records. — All level notes must be recorded directly in book 
9-903. Under no circumstances should separate pieces of paper be 
used for figuring or for temporary records. Use ink or No. 4 pencil, 
make all figures distinct, and do not crowd them. When two impor- 
tant bench marks come close together provide ample room for placing 
their written descriptions opposite the appropriate figures by drop- 
ping the figures for the record one or more lines down the page. 
For a given H. I. (height of instrument) the rodman 's notes must be 
at least two lines lower down the page than the levelman 's and they 
must not turn over a leaf at the same time. Erasures with rubber or 
knife are not permissible under any circumstances; a single line 
should be drawn through an erroneous record and the corrected fig- 
ures written above it. The flyleaf of each notebook must be prop- 
erly filled in when the book is first used. 

Both the levelman 's and the rodman 's books must be balanced 
daily. At the bottom of each page, and at the end of the day's work, 



INSTRUCTIONS TO TOPOGRAPHERS. 59 

each column of fore and back sight distances and readings should 
be shown to agree with the difference of elevation previously com- 
puted. This check must never be omitted and the computation 
must appear on the page opposite the notes. Side sights which are 
not a part of the continuous line should be recorded in an extra 
column or within brackets. 

PRIMARY LEVELING WITH YARD ROD AND PRISM LEVEL. 

Personnel. — A prism level party consists of one levelman, two 
rodmen, a recorder, and an umbrella man. 

Instruments, notebooks, etc. — The instruments and outfit consists 
of the following: 

One prism level. 

Two yard rods, each to have plumbing level and thermometer attached. 

One steel tape (25 feet). 

Two steel turning-point pins, hollow head. 

One Locke level. 

One umbrella with staff. 

One set dies (figures and letters). 

Bench-mark tablets or posts. 

Copper nails and washers for temporary bench marks. 

Cement, paint can, keel, and other accessories. 

Two book bags. 

Prism level notebook 9-940. 

Bench-mark description book 9-916. 

Character of lines. — Primary levels executed with a prism level 
need be run in only one direction, but must be in circuits or other- 
wise checked. 

Accuracy. — Circuits must close with an error in feet not exceeding 

0.04 -^length, of circuit in miles, 
which is equivalent to 

0.056 -^/distance between bench marks in miles 
for forward and backward lines. 

Graduation of rod. — The rod used is graduated to yards, tenths, 
and hundredths, and is read by estimation to thousandths. Each 
yard has a different and distinctive color, which must be recorded 
for each reading. One edge of the rod has also graduations in feet 
and tenths for use as a check on yard readings. 



60 INSTRUCTIONS TO TOPOGRAPHERS. 

Ratio of wire intervals. — The rod is read with each of the three 
horizontal wires in the instrument. The mean of the two wire 
intervals in thousandths of a yard as read upon the rod should equal 
the distance to the rod in feet, but this should be tested. As the 
upper and lower wires are not always equidistant from the middle 
wire, the ratio of the wire intervals must be determined from the 
first day's level notes for use as specified in the next paragraph. 

Methods of reading. — The program at each set-up is as follows: 
After the tripod is firmly set and the clamp screws tightened, level 
approximately by the circular level, which has been adjusted by 
comparison with the long level. Point the instrument toward the 
rod and clamp ; bring the level bubble to the center of the tube by 
means of the micrometer screw. Read on the rod, and first call off 
the color initials for the lesser and greater extreme readings; second, 
call yards and tenths for each wire, taking the smallest reading first; 
third, repeat and read yards, tenths, hundredths, and estimated 
thousandths; fourth, for additional check on the yard number, 
read the middle wire on the tenths of feet scale on the back of the 
rod. Before the level is moved the recorder should first see that 
the color agrees with the yard readings; second, he must compute 
the two wire intervals and if their ratio one to the other differs more 
than i per cent from the true ratio (see preceding paragraph), the 
levelman must repeat the readings; third, he must compute the 
mean reading in feet by summation, and test units and tenths by 
mentally multiplying the middle reading by 3, also by comparing 
with the reading on the scale on the back of the rod. An agreement 
must be reached before the next sight is taken. The temperature 
must be recorded for each hour. 

Level adjustment. — When the work is commenced, and at least 
once each day thereafter, the adjustment of the level must be tested 
by the "peg method" as follows: 

At some convenient set-up, after the usual back-sight and fore- 
sight readings have been recorded, copy the fore-sight on a separate 
line as a new fore sight apart from the leveling record, leave the 
fore-sight pin in place, and set a second turning pin about 30 feet 
back of the instrument; read rod on it for a new back sight; find 






INSTRUCTIONS TO TOPOGRAPHERS. 



6r 



from these the mean readings in feet as usual. Move the level for- 
ward to a set-up about 30 feet back of the fore-sight pin and take 
readings on the fore-sight pin and then on the back-sight pin. The 
constant "C," which is a factor of the adjustment correction, must 
then be determined thus: Sum of readings on near rods minus 
that on far rods, corrected for curvature and refraction in feet, 
dividedlDy three times the difference between the sum of the greater 
and that of the lesser rod intervals in yards. 

The rod interval for any sight is the difference of extreme wire 



readings. 



Example of computation of C. 



[To be made in the field.] 



Determination of C, 8.20 a. m. August 28, 1910. 



Thread 
reading. 


Thread 
interval. 


Sum of 

thread 

reading. 


Height 

of instru- 
ment. 


Sum of thread 
reading. 


Thread 
interval. 


Thread 
reading. 


i-5i5 
1.528 

1.542 

2.252 
2-357 

2.462 
The fractic 


0.013 
.014 


4.585 

7.071 
1.385 


1. 101] 
Dr far-rod c 

1 


1.386 

3.865 
4.585 


0.105 
. 104 


0.357 
.462 

.566 

1.276 

1.288 

1. 301 


.027 

• 105 
.105 


. 209 

.012 
• 013 


. 210 
. 209 


• 025 


.025 
.027 


.419 
• 052 


8.456 
—0. 0005 


8.450 
8-4555 


• 052 


■ 367 yds. 
3 


8-4555 
eet=sum f 


— • 0055 (—0.005 
listances. 


1. 101 ft. 

.419 ! 

n~ ~ '=210 i 
. 002 



For correction to be applied to the sum of readings on distant rods 
for curvature and refraction, see table in back of field book 9-940. 



62 INSTRUCTIONS TO TOPOGRAPHERS. 

When the sum of the readings on the near rods is the greater, the 
sign of C will be plus, and vice versa. Great care must be taken in 
pointing off decimals and in giving proper signs. 

Adjustment of bubble. — If the resulting value for C numerically 
exceeds 0.005, an adjustment should be made by changing the po- 
sition of the level bubble only, as follows: 

Point to a distant rod with the bubble in the middle of the tube 
and read; move the telescope (by micrometer screws) so as to 
raise the middle cross wire by an amount which in yards is equal 
to C times the extreme wire interval. While holding the telescope 
in this position, bring the bubble to the middle of the tube by 
raising (or lowering) one end of the level vial with the adjustment 
wrench; if C is negative, the middle wire must of course be lowered 
on the rod. After the adjustment has been made, its accuracy 
should be tested by redetermining the value of C. 

In case the cross wires break and the level-tube adjustment has 
not been disturbed, insert new spider threads and determine a 
value of C, as above directed. Compare with the last determina- 
tion of C, and adjust for the difference by changing the position of 
the ring only — not the level bubble. 

Care of instrument. — When the level is on the tripod, be sure that 
the central tripod clamp screw is tight. Keep the telescope off the 
micrometer-screw bearing while carrying it between stations. 
Leave the three tripod wing nuts loose when carrying; clamp tight 
when tripod is in place for work. 

The level must be shaded by an umbrella when in use and by a 
cloth hood when carried between stations. In rough country the 
place to set up the rod or level can be quickly found by means of a 
hand level. 

Care of rods. — The rods must always be kept covered when not in 
use. Never let painted sides touch the ground. Should difficulty 
be found in holding a rod steady because of wind, two pieces of 
bamboo or other light poles, 8 feet long, may be held by the rodman 
against the rod, so as to make a triangular brace against the wind. 
Plumbing levels must frequently be tested and kept in adjustment. 



INSTRUCTIONS TO TOPOGRAPHERS. 63 

Testing of rods. — At the beginning and end of the season and at 
least twice each month during the progress of the leveling the inter- 
vals between the metallic plugs on the face of each level rod must 
be measured carefully in feet to the nearest thousandth, always 
with the same steel tape, kept for that purpose. The temperature 
must also be recorded and the number of the tape. 

Length of sights. — The length of fore and back sights must be 
equalized with the prism level as with the Y level. The maximum 
length of sight with the prism level is 360 feet except at river cross- 
ings. Sights across broad river crossings should be taken in the fol- 
lowing manner : 

Mount the instrument and place stakes so that the center wire 
will fall near the middle of each rod; if the distance is too great to 
read the three wires, use improvised targets of cardboard held in 
place by rubber bands or other simple device, and make several 
settings by raising and lowering them an equal number of times. 
Rodmen should be provided with field glasses if necessary to read 
signals. From bench marks on each bank the elevation of the 
adjacent water surface should be determined as an additional check . 

Record. — The notes are to be kept in ink in book 9-940, as for 
precise leveling (p. 65), except that each H. I. and level should be 
computed. No erasures are permitted, either with rubber or knife ; 
a single line should be drawn through erroneous records. Extra 
fore sights when made should be recorded in the special column on 
the right-hand page, opposite the H. I., and recorded with " back- 
ward," "forward," "right," or "left" added to show the direction 
to the rod from the instrument. 

Computations required must be made at the bottom of each page 
each night, or oftener if convenient, by both levelman and recorder 
independently . 

On primary work the algebraic sum of the page excesses of back 
sights or fore sights for each day should be written in the lower 
right-hand corner of the right-hand page. Three times the sum 
of the second of each group of three readings in column 1 of the note- 
book, plus the algebraic sum of the excesses of the lower over the 
upper thread intervals in column 2, should equal the sum of the 
mean feet readings in column 3, similarly with columns 7, 6, and 5. 



64 INSTRUCTIONS TO TOPOGRAPHERS. 

The difference (column 3 minus column 5) should be written at the 
bottom of column 4 and should equal the difference obtained by 
subtracting the first from the last elevation, which should be written 
in the upper space at the bottom of column 4. 

The formula 3 C (column 2— column 6), etc., at the bottom of the 
right-hand page is for computing the correction to the elevations 
for combined errors of level and collimation. This computation 
need not be made in the field. C is the constant which results 
from the "peg method" test of adjustment. By "(column 2 — 
column 6)" is meant the difference of the continuous sums of the 
rod intervals of columns 2 and 6. 

PRECISE LEVELING. 

For precise leveling the instrumental outfit and the number of 
men in the party are the same as for primary leveling with prism 
level, but the following modifications of methods must be made: 

Iyines must be run independently in both the forward and the 
backward direction. The allowable error in feet is 

0.017 V distance between bench marks in miles, 

and when this limit is exceeded on any section the forward or back- 
ward measure is to be repeated until a pair run in opposite direc- 
tions is obtained between which the divergence falls within the 
limit. It is especially desirable to make the backward measure- 
ment in an afternoon if the forward measurement was made in the 
forenoon, and vice versa. The observer should make the two 
measurements under atmospheric conditions as different as possible 
without materially delaying the work for that purpose. At alter- 
nate stations the fore sight is to be taken before the back sight — 
that is, always take readings on the same rodman first. 

The maximum allowable difference between a back sight and 
the corresponding fore sight mean thread interval is 0.033 yard 
(33 feet distance). The continuous sums of rod intervals for the 
section between bench marks must not be allowed to differ more 
than 0.132 yard (66 feet distance), and they should be kept as nearly 
equal as possible. 



INSTRUCTIONS TO TOPOGRAPHERS. 65 

The last set-up of one running must not be copied nor used as the 
first set-up of a return running — that is, the instrument must be 
moved so that an independent reading can be obtained. 

If any measure over a section differs more than 0.02 foot from the 
mean, that measure must be rejected. No rejection shall be made 
on account of a residual smaller than 0.02 foot. 

Whenever a blunder, such as a misreading of 1 yard or one-tenth 
or an interchange of sights, is discovered and the necessary correc- 
tion is applied, such measure may be retained, provided there are 
at least two other measures over the same section which are not 
subject to any uncertainty. 

When commencing work for the day and at the beginning and 
ending of each section record the time. Record the temperature 
for each set-up, using thermometer readings alternately for each rod, 

It is not necessary to complete the H. I. and elevation column, 
but the difference of elevation for each section should be computed. 

The field computations of precise work must be made as the work 
progresses, on forms provided for this purpose. When original 
records are completed in the field send them immediately to the 
chief geographer, Washington, D. C, by registered mail, retaining 
the C3rresp3nding forms until notice is received of the receipt of 
the original records. 

SPECIAL INSTRUCTIONS FOR USE OF PRISM LEVEL NOTEBOOK Q-940 
WHEN USED FOR PRIMARY OR PRECISE LEVELING RECORD. 

Fill in the blanks on the flyleaf the first day the book is used . 

Fill in the blanks at the head of each page each day, on precise 
work, indicating bench marks run between by their letters or 
numbers. 

Each horizontal space between two red lines is for a single set-up 
of the level. 

The notes for each section of line on precise work must be complete 
in themselves and commence on a new page. Every primary line 
record must begin on a new page, and the initial bench mark must 
be fully described. 
8221 — 11 ? 



66 INSTRUCTIONS TO TOPOGRAPHERS. 

The columns being counted from the left, each is used as follows: 

Column i is for the readings on the rod in yards for the three 
threads, each set of readings to occupy a separate space between red 
lines, the first recorded reading being for the wire giving the smallest 
value. The color letter is to be placed beside the first and last 
readings. The recorder should notice whether the color as recorded 
corresponds with the unit called out by the levelman. Each day 
the levelman should verify the comparison and, if a discrepancy 
exists, rerun the section. 

Column 2 is for the thread intervals for the thread readings in 
column i, the upper ones being the difference between the lowest 
readings and the middle ones, the lower being the difference between 
the middle and the greatest readings of each set. (See also para- 
graph following.) 

Column 3 is for the sums of the three-wire readings of each space 
in column i, between the horizontally ruled red lines, these sums 
being equal to the mean in feet of the three readings on rod. 

Column 4, with the exception of the last line, is not intended for 
use in precise leveling, but can be used to compute approximate 
elevations, being filled out only at bench marks. On primary work 
the first entry on the page at the left of the words " Elevation brought 
forward from page — ' ' should be the elevation from a previous page, 
or from another book. In the latter case, give book number and 
page, and always carefully verify the copying. The second entry, 
below the red line and above the short black line, is the height of 
the instrument as found by adding the first entry in column 3 to the 
first elevation in column 4. The third entry in column 4 is the ele- 
vation computed by subtracting the first fore sight from the H. I. 
In each case the H. I. will always be above a short black line and the 
elevation always just above a red line. 

The records in columns 3 and 5 should be placed on line with the 
H. I. 

Columns 5, 6, and 7 are for fore-sight readings, corresponding with 
3,2, and 1 for back-sight readings. 

Column 8 is for the record of temperature and time. 

Column 9 is for the correction of curvature and refraction for un- 
equal sights and need not be filled out in the field. 



INSTRUCTIONS TO TOPOGRAPHERS. 67 

Column 10 is for extra fore sight at points which are not turning 
points, also for their sum. 

Column 11 is for description of bench marks, for elevations from 
extra fore sights, for transcripts of bench-mark elevations, and for 
general remarks or explanation. 

In columns 2 and 6 write next above the red lines the continuous 
sums of the rod intervals for the section. The mean of the last pair 
of continuous sums in columns 2 and 6, multiplied by 1,000, will be 
equal to the distance in feet for the page; its equivalent in miles 
and tenths can be obtained from the table in the back of the book. 
The total mileage from the beginning of the section on precise work 
and of the line on primary work must be given at the bottom of each 
right-hand page. 

A sample page from a field book follows: 



68 



INSTRUCTIONS TO TOPOGRAPHERS. 



-a a 

■ugci 
rt aS > 

o> a> en 



^ 



N<> 



i 



o 



CQ 






X « 



5 8* 






CM 



s 

o 

ft 



SI 



""8*3 

ft 






as ft* 



H k, H 
CM ^ts. 



04 04 



«*>> o> > 

en ^^ 



04 fti 



CM M 
CM CM 



CM CM Ov 



CM CM \h 






It 

ft£ 



o 



fc 



fil 



CM CM 



CnO>> 
CM ^O N 
C^ ^°o 



04 



K, CM ^ 

CM CM Ov 



COON 
O CM «^ 



ftj X 



CM H N, 

CM CM > 



CM \h «0 

Oo CM ^O 
0r>\0»0 



04 04 



CM CM Oq 



c^ ^ ts. 



04 04 



INSTRUCTIONS TO TOPOGRAPHERS. 



6 9 



<» ? S 



• si • © 



1 



o> 


°o K 


,» 


«^VS 


BO 


O M 



M 



U 






© ^ 

CM 00 






+ I 



CO 



> o> 



rn C 






O 


II *~ 


1 8 


<U 


U-t 




2~ ^ 


■M 


CNJXO 

ts.00 





<*> H 




II 


.3 


vL ll .2 




^s^a 


Col. 
total 
-Co 
d colli 


~ ..,-3 c8 


N $o~ 


3'iol 






CO oo 

I H 

CO I 



00 


(^ 


> w 


<n 













VD 




3 I 



7<3 INSTRUCTIONS TO TOPOGRAPHERS. 

COMPUTATION AND ADJUSTMENT OF LEVEL CIRCUITS. 

The computation of each line is first checked to be sure that the 
proper corrections have been made for errors of rods, including those 
due to changes in temperature, and for errors due to unbalanced 
sights as affected by curvature and refraction. Corrections are then 
made for systematic errors for which the law may be known, such as 
that necessary to take account of the fact that water levels along a 
meridian at different altitudes are not parallel curves, except at the 
equator and at the poles. This correction depends on meridional 
distance, latitude, and altitude, and is called the orthometric cor- 
rection; it may be found from the following approximate formula: 

n _ h m (^2-^l) sin (^t+W 



in which 



660,000 



C= correction in feet. 
£m=mean height of line in feet. 
<j> x and 2 =are the latitudes of the south and north ends of section, respectively. 
(02—^)= difference of latitude in minutes of arc. 

In applying the formula the lines must be divided into sections 
of not over 100 miles each, and a division should be made where the 
general direction changes materially. The corrections thus found 
are applied to the several sections so as to lower the elevations at 
successive division points going northward. Although orthometric 
corrections at times lead to apparently absurd results, such as giving 
a lower elevation for the north end of a large lake having no outlet 
than for the south end, yet in order to insure agreement between 
different lines and to obtain results of the greatest theoretical accu- 
racy, they must be applied when appreciable. 

After all the foregoing corrections are made to the original results, 
the remaining closure errors are those which are to be removed by 
adjustment. 

Precise. — Weights are first assigned for each class of levels, and 
observation equations are formed and solved by "least squares." 
In this manner every line helps to establish the elevation for each 
junction point. When all the junction points are fixed the correc- 
tions are distributed over the lines in proportion to distance. 

Primary. — The Geological Survey in adjusting primary levels has 
adopted a method which may be described as follows: 



INSTRUCTIONS TO TOPOGRAPHERS. 7 1 

All adjustments are to be made in the bench-mark description 
book 9-916, in which abstracts from the field books, which include 
the description and elevation of each point as determined by the 
levelman, are written by him in regular order for each line as run. 

All the level lines associated with one another should be con- 
sidered at one time, and in order to better comprehend their arrange- 
ment they should first be platted on the office progress maps as 
accurately as possible and from these tracings should be made on 
paper, to be used in the adjustment and later filed with the descrip- 
tion book as part of the record. The plat should show the approxi- 
mate relation of all the lines, including the precise or previously 
adjusted lines forming the base of the system, and the work of differ- 
ent grades or different men should be represented by differently 
colored inks or pencils or in some other manner, a suitable explana- 
tory legend being attached. The names of a sufficient number of 
towns should be given to identify the location readily, and beside 
each line reference should be made to the page in the description 
book where the bench-mark elevations for that line are given. On 
each line a > is to be placed to show the direction in which it was 
run. For small areas the diagram of routes prepared by the levelman 
in the description book will probably answer in place of the tracing. 

The field notes should be examined to see whether the work was in 
accordance with the instructions; whether fore and back sights were 
equalized, rod readings properly summed, balances checked, and 
elevations properly copied from page to page. The entries in the 
description book should be systematically checked to see that all 
elevations, including those at starting, junction, and closing points* 
and all breaks and second runnings are properly copied. Where 
two runnings of equal weight are made over one course the mean 
result should be accepted for adjustment and written in red ink 
with the appropriate statement in the "unadjusted elevation" 
column, the divergence being given in the margin. 

At each junction point on the diagram should be written the 
difference between the recorded elevation by some one of the lines 
and those recorded in the description book for each of the other lines 
for the same bench mark, with an arrow alongside and plus or minus 
signs added to indicate that the elevations as brought by these lines 



72 INSTRUCTIONS TO TOPOGRAPHERS. 

are greater or less than the assumed one. Also, as an additional aid 
in the adjustment, the closure error for each circuit should be written 
in the center of its plat on the diagram, each amount and sign being 
computed in counter-clockwise order. Next ascertain by inspection 
of the diagram which of the unknown junction points may be deter- 
mined with the greatest apparent accuracy or by the greatest num- 
ber of independent lines. From two or more lines connecting this 
point with the points of known elevation obtain two or more possible 
corrections to the assumed elevation. Estimate and record relative 
weights for these corrections, the weights to be based on length of 
lines (usually in inverse proportion to their length), class of leveling 
instrument used, number of times leveled, and in rare cases on rela- 
tive standing of observers if two are involved. Weights should not 
be influenced greatly by closure errors. Where corrections from 
different sources have a line in common, the length of this line 
should be doubled in fixing the weights of each. 

From the weights adopted compute the weighted mean correction 
to the assumed elevation of the new point as follows: Multiply the 
correction computed for each of the independent lines from known 
points in turn by the weight of the line from which each was deter- 
mined ; divide the algebraic sum of these products by the sum of the 
weights. The quotient is the correction to apply algebraically to 
the assumed elevation; it should be written in the diagram at the 
proper junction point in a small loop or rectangle with the letters 
" Cor. " and the plus or minus sign. In complicated nets it may be 
necessary to assign a preliminary correction to a junction point in 
order to carry a correction from it to some other point; after fixing 
the correction for the second point from its various lines a final 
correction is determined and substituted for the preliminary value 
of the first point. 

In this manner weighted values are found for each junction point 
in turn, and between the points thus fixed corrections are distributed 
in proportion to the distance. A line or point once thus adjusted 
should not be readjusted unless readjustment is required by new 
field data. 

Figure 2 is given as an illustration of the method of adjusting a 
level net. By inspection of the diagram, junction point E appears 



INSTRUCTIONS TO TOPOGRAPHERS. 



73 



to be the most favorably situated for adjustment first. The line run 
from A via B and E to D closed at D 0.250 foot low; from H via I to E 
0.500 foot low. The elevation brought from source A is at first 
assumed for the adjustment as having a correction of o. The cor- 
rections brought from sources D and H will then be +0.250 and 
— 0.500, respectively. The distances to be used in assigning weights 



10 



are taken as A via B to E=— +8=13 miles (A to B, being a double- 

2 

run line, must be given double weight, which is done by dividing 

the length of the line by 2); D to E, 5 miles; H via I to E, 10 miles. 




Figure 2. 

The weights to be assigned should be in inverse proportions to the 
length of the lines, or nearly so. To determine the weights, divide 
any convenient number — as 13 in this example — by the computation 
distances 13, 5, and 10 each in turn, obtaining 1, 2.6, and 1.3 for the 
weights of the respective lines. These weights are each to be mul- 
tiplied by the corresponding assumed corrections o, -{-0.25, and 
— a.50, giving products of o, -fo.65, and —0.65. Divide the alge- 
braic sum of these products by the sum of the weights (4.9), the 
quotient will be the weighted correction; this is o for the point in 
question, but as there is another line to this point which has not 



74 



INSTRUCTIONS TO TOPOGRAPHERS. 



been considered this correction must be accepted as preliminary 
only. The foregoing data may, if desired, be assembled in tabular 
form, thus: 



From 
point — 


Miles. 


it r~; ~w Correc- 
Weight ' ! tion. 


Weight 
X cor- 
rection. 


A... 
D.... 
H.... 

Sura . 


13 

5 
10 


1.0 0.000 

2.6 + . 250 
1.3 - .500 


0.00 
+ .65 
- -6 S 




A. Q 


.00 




4 9 | 



Junction point B may be considered next. The preliminary cor- 
rection for this point is taken as o, as found from three lines, two lines 
from A and one from B. A preliminary correction of +0.1 foot for 
I can be obtained by taking a proportionate part of the closure error 
at B (one-fifth). Junction point F depends for its elevation on 
values from several lines. The corrections from K, B, and I are, re- 
spectively, o, —0.32, and —0.18; the corresponding distances are 12, 
10, and 26; the weights 2.2, 2.6, and 1.0; the resulting preliminary cor- 
rection for F is —0.18. A final value for K may now be found from 
B, D, I, and F; this is necessary to include the effect of F^ and by the 
foregoing method it is found to be —0.03 . G is found from lines from 
B via C, F, F via C, F via J, and I, with the computation distances s^> 
7, 44, 28, and 38, respectively; in this case the distances C to G and J to 
G, which are common to two lines, should be doubled in order not to 
give them undue weight. The final corrections to the assumed ele- 
vations are now found in a similar manner, the computations for B, 
I, and F being repeated to secure the effect of the additional lines, 
and are as folio ws : B, 0.00; C, — 0.30; E, —0.03; F, —0.18; G, —0.38; 
I, +0.09; and J, —0.18, two places of decimals only being used for 
junction points. Bach of these corrections is placed in a rectangle 
on the diagram near the point to which it belongs. 

After the corrections for the junction points are. fixed, corrections 
proportioned to the distance are found for intermediate points along 
the several lines. 

I/ines on which the closure error is much over the permissible limit 
must be omitted in adjustment; they may be tied in afterwards, but 



INSTRUCTIONS TO TOPOGRAPHERS. 75 

in publishing the results a statement must be made cautioning 
engineers against dependence on them. If gross errors are evident, 
the results must not be published until the lines are rerun. 

For long north-south lines n high altitudes, the orthometric cor- 
rection should be applied (p. 70). 

The computer should report to the division geographer in writing 
any failure on the part of the levelman to comply with instructions; 
he should also report all circuit-closure errors in excess of the allow- 
able limit (pp. 57, 59, and 64). 

ADJUSTMENT OF INSTRUMENTS. 

The object glasses and eyepieces of all instruments must be prop- 
erly focused. The cross wires projected against a distant object 
should appear immovable when the eye only is moved. Before the 
adjustments are commenced the instruments must be firmly set up 
and leveled. An instrument may at times appear to be out of ad- 
justment because some part is loose. The object glass may be 
partly unscrewed or an adjusting screw may be only partly tightened. 
Iyevel bubbles or cross wires occasionally become loosened; there- 
fore, before commencing the adjustment of an instrument look out 
for such defects. When it is thought that an adjustment has been 
completed, always test it before using the instrument. All adjusting 
screws should be screwed tight enough to hold, yet not so tight as 
to injure the threads or put a severe strain on any other part. Ad* 
justments should be made in the order given, for many adjustments 
depend on the accuracy of others previously made; sometimes two 
or more adjustments must be made simultaneously, as a change in 
any one affects the others. 

TELESCOPIC ALIDADE. 

But two adjustments are required for the telescopic alidade — for 
level and for collimation. These should be tested daily. 

Level. — Clamp the telescope, bring the bubble to the center of the 
tube with the tangent screw, lift up the level carefully, reverse, and 
replace it on the telescope. If the bubble runs away from the center 
bring it halfway back by means of the tangent screw and the other 



76 INSTRUCTIONS TO TOPOGRAPHERS. 

half by the adjusting screw under the end of the level tube. Repeat 
this operation till the bubble stays in the center after reversal. 

Collimation. — Point the telescope on a small but well-defined 
object about half a mile distant, and while watching this through 
the telescope revolve the telescope 180 in its supporting sleeve. 
If the intersection of the cross wires remains centered on the object 
the adjustment is perfect; if not, change the cross wires for half the 
error and repeat the operation until they stay on the point selected. 
A slight shift in the position of the cross-wire ring should be made 
if necessary to make the vertical wire parallel to the vertical corner 
of a building or a plumb line. 

Ruler. — So long as but a single alidade and but one edge of the 
ruler are used it makes no difference in the results whether the edge 
of the ruler is parallel to the line of sight or not. 

Y LEVEL. 

All instrumental errors of the Y level can be eliminated by exactly 
equalizing fore and back sights, but as this is seldom possible the 
line of collimation and the level should be kept as nearly in adjust- 
ment as practicable. 

Level. — Having the instrument carefully leveled, loosen the clips, 
lift the telescope out of the Ys, reverse it end for end, and replace it 
in the Ys; if the level bubble has moved away from the center bring 
it halfway back by means of the adjusting screws at one end of the 
level tube and the other half by the lower leveling screws. Repeat 
this operation until the adjustment is perfect. With the bubble in 
the center, rock the telescope back and forth in the Ys about 25 ° 
around its axis; if the bubble moves away from the center bring it 
back with the side adjusting screws. 

Collimation. — Having the instrument carefully leveled, note a 
small object about 300 feet distant that one end of a horizontal cross 
wire touches, turn the instrument on its vertical axis a few degrees, 
and note whether the other end of the cross wire cuts the point; if it 
does and the Ys are not badly out of adjustment the wire is horizontal . 
With the clips up, focus on a small object 300 or 400 feet distant ; watch 
this through the telescope while revolving it 180 in the Ys; if the 
intersection of the cross wires moves away from the point bring it 



INSTRUCTIONS TO TOPOGRAPHERS. 77 

halfway back by means of the cross- wire adjusting screws; repeat 
the test and adjustment until there is no movement of the cross wires 
away from the point. 

Object-glass slide. — It is seldom necessary to adjust the object-glass 
slide, as it is usually fixed by the maker, but when required make 
the collimation adjustment as above described; then an error in the 
adjustment of the slide will appear as an error of collimation when 
tested on a near-by point, say 50 feet distant. To correct the error 
remove the ring near the middle of the telescope and with a screw 
driver turn the screws found underneath so as to bring the cross-wire 
intersection halfway back to the near-by point selected 

Eyepiece slide. — The adjustment of the eyepiece tube so that the 
cross wires will appear in the center of the field, though not essential 
to the accuracy of the work, may be effected by means of the screws 
underneath the ring just back of the cross- wire screws. Loosen one 
and tighten the opposite one of these screws with a screw driver until 
the wires appear centered. 

Ys. — After each of the foregoing adjustments have been made, 
the adjustment of the Ys is made by turning the telescope and level 
180 on its vertical axis; if the level bubble, which was at first in the 
center, moves away from it, bring it halfway back by changing the 
large nuts under one Y. 

"Peg method." — In the ordinary Y level adjustment it is assumed 
that the two rings on the telescope tube which rest in the Ys are 
circular and exactly equal by construction. 

The level and line of collimation can be made parallel independ- 
ently of the rings and Ys by the "peg method" described under the 
heading "Prism level" (p. 60). 

LOCKE LEVEL. 

The adjustment of the hand level or Locke level is most easily 
tested by sighting along a horizontal line determined by a Y level 
or alidade, but when no such line is available, a modified form of the 
"peg method" must be used. Hold the level on a fixed point and 
sight a second point 300 or 400 feet distant which appears by the level 
being tested to have the same elevation as this point. Take the 
level to the second point and with the bubble centered over the cross 



78 INSTRUCTIONS TO TOPOGRAPHERS. 

wire sight the first point; if it appears to be on the horizontal line 
the level is in adjustment; if not, correct for one-half the difference 
by turning the small screw at one end of the level box. 

ROD LEVEL. 

The leveling or stadia rod to which levels are attached should be 
carefully plumbed with string and plumb bob. The level bubbles 
should then be brought to the centers by means of the proper adjust- 
ing screws. 

TRANSIT. 

Plate levels. — After leveling carefully revolve the instrument 180 
on its vertical axis. Bring each level bubble halfway back to the 
center of the tube by means of the screw at one end. 

Collimation. — Level carefully, sight on a point about 500 feet 
distant, raise or lower the telescope slightly, and note whether the 
vertical wire remains on the point; if not, loosen the capstan-headed 
screw and turn the cross-wire ring till the vertical wire will remain 
on the point when the telescope is raised or lowered. Clamp the 
instrument, set the vertical wire so that it cuts the point selected, 
transit the telescope by revolving it 180 on its horizontal axis, and 
select a second point 500 feet distant in the opposite direction from 
the first. Unclamp the upper plate, turn the transit 180 on the 
vertical axis, set it on the point first selected, and again clamp the 
plate. Transit the telescope and if the vertical cross wire exactly 
bisects the second point the adjustment is perfect; if it does not, 
bring it one-quarter of the way back to the second point by turning 
the two capstan-headed screws on the sides of the telescope . 

Standards. — Set up the transit near a tall building or other high 
object; after leveling carefully point the telescope so that the vertical 
wire intersects a definite point about 6o° above the horizontal, de- 
press the telescope, and select a second point near the ground. 
Unclamp the upper plate, revolve the telescope and plate 180 on 
the vertical axis, clamp the plate with the vertical wire again cutting 
the upper point, and depress the telescope; if the cross wire inter- 
sects the lower point the standards are in adjustment; if it does not, 
correct for one-half the error by the screw underneath one end of the 
telescope axis. 



INSTRUCTIONS TO TOPOGRAPHERS. 79 

Object-glass slide. — If an adjustment for the telescope object-glass 
slide is possible, it is made as follows: First make the collimation 
adjustment for a point about 300 feet distant, then focus on a point 
1,000 feet or more distant and again on a point only 10 or 15 feet away, 
transit the telescope, unclamp the plate, turn it 180 on the vertical 
axis, and reclamp. If the cross wire still cuts the distant and near 
points the slide is in perfect adjustment, but if it does not, correct 
half the error by means of the side screws which hold the slide ring 
in place. Next repeat the regular collimation adjustment and again 
test for the slide error; repeat both adjustments until no errors appear * 

Eyepiece tube. — The eyepiece may be put into position over the 
cross wires by turning the screws which hold the eyepiece ring until 
the cross wires appear in the center of the field; an exact centering 
is not required. 

Telescope level. — If there is a level attached to the telescope it may 
be adjusted by the "peg method" after all the other adjustments are 
made, as follows: Level the transit and bring the bubble to the center 
of the tube under the telescope. Take a reading on a leveling rod or 
pole 300 or 400 feet distant, which is held on a stake set firmly in the 
ground. Revolve the transit 180 on the vertical axis and after 
again bringing the bubble to the center set a second stake at the 
same distance as the first and at such an elevation that the rod or 
pole reading is the same as on the first stake. The tops of the two 
stakes will then be at the same elevation. Move the transit 25 or 50 
feet back of one stake and on a line with the other. Make the tele- 
scope as nearly horizontal as possible by means of the attached level, 
clamp it, and then take a reading on the rod held on the near stake 
and another reading on the distant stake. If the two readings agree 
the telescope is horizontal; if they do not agree turn the tangent 
screw so as to bring the cross wire while set on the distant rod nearly 
to an agreement; repeat the operation till an agreement is reached. 
The telescope is then level and the adjusting nuts at the end of the 
level tube should be turned till the bubble is brought to the center. 

Vertical circle or arc. — The screws holding the vernier for the 
vertical arc should now be loosened and the vernier moved until the 
reading is o° while the telescope is still level. 



80 INSTRUCTIONS TO TOPOGRAPHERS. 

THEODOLITE. 

Striding level. — Place the level in the proper position on the 
telescope axis. Level carefully with the horizontal plates clamped 
and rock the level slowly back and forth till the foot pieces strike. 
If the bubble leaves the center, bring it back by means of the side 
adjusting screws near one end of the tube. 

Reverse the level and bring the bubble halfway back to the center 
by raising or lowering one end of the tube with the screw at that end, 
and the other half with the leveling screws. Repeat these operations 
till the adjustment is perfect. 

Standards. — After the striding level is in adjustment with the 
lower horizontal circle clamped, level the instrument in two positions 
at qo° from each other. Turn on the vertical axis 180 from one 
position; if the bubble runs away from the center bring it halfway 
back by loosening one of the large capstan-headed screws underneath 
the standards and tightening the other. Test the adjustment and 
repeat it if necessary. 

Plate levels. — Level instrument with the striding level only, then 
bring the bubbles of the plate levels to the center of their tubes by 
means of the end adjusting screws; or the method described for 
adjusting the transit plate levels may be used for the theodolite also. 

Micrometers . — Each micrometer consists of three concentric tubes; 
the upper and lower ones slide in the central one. The lower tube, 
which holds the object lens when in proper position, is clamped to 
the middle one by means of the capstan-headed screw in the lower 
part of the J-shaped support. These two tubes may be moved 
together or the lower one moved alone by loosening the proper screws. 
The upper tube contains the eyepiece lenses and is held in place by 
friction only. 

Focus the eyepiece on the two parallel movable threads and do not 
change it afterwards . With the eye in position for setting the microm- 
eter, tighten one and loosen the other of the two screws that hold 
the ]-shaped microscope support to the main frame of the theodolite, 
until the figures and graduations on the plate appear to be in the 
center of the field. 

Clamp the plate and by turning the micrometer screw set the two 
movable threads over a long graduation. Examine carefully to see 



INSTRUCTIONS TO TOPOGRAPHERS. 8 1 

whether they appear exactly parallel to it. If they are not parallel, 
loosen the two capstan-headed screws which clamp the micrometer 
tube and twist the tube until the threads and mark appear parallel. 
Clamp the side screws lightly. 

Set the movable cross wires on a division to the apparent left of the 
field of view as for a regular angle reading; read the micrometer head 
and record the reading. Turn the graduated head about five turns, 
stopping when the threads are set on the next io' division to the right; 
read and record. Repeat this operation several times. If the mean 
of the left-hand readings is the same as the mean of the right-hand 
readings, or within one division of it, the adjustment may be 
accepted as satisfactory. An actual count of full revolutions should 
be made at least once; otherwise the adjustment might wrongly be 
thought perfect for 4^ or 5^ revolutions. • 

When the space covered by the two parallel micrometer threads, 
moved by exactly five revolutions of the micrometer screw, appears 
to be longer than one io' space on the graduated circle, to bring it 
into adjustment make the distance between the micrometer box and 
graduated plate longer by raising the middle part of the tube; but 
when the space is shorter than aio / space make that distance shorter 
also — that is, consider as connected or dependent the length of the 
thread space covered by an even five revolutions of the micrometer 
screw and the distance between the micrometer box and the gradu- 
ated plate. When the former is longer than it should be, the latter 
should be made longer, if an adjustment is desired, and vice versa. 

To make the adjustment, loosen the small capstan-headed screws 
which clamp the microscope tube; then, if the thread space is long, 
twist the middle part of the tube (including the micrometer box) 
back and forth and at the same time pull it upward, thus lengthening 
the distance to the graduated plate. When by estimation it has 
moved far enough, which can be roughly determined by the amount 
of blurring that results from the lower lens being thrown out of focus* 
clamp the upper capstan -headed screw. The lower part of the micro- 
scope tube holding the objective lens must now be twisted and gently 
pushed downward till the graduations again appear in focus. If the 
movable threads and graduations are not then parallel, the upper 
screw must be again loosened and the tube turned far enough to make 
8221 — 11 6 



82 INSTRUCTIONS TO TOPOGRAPHERS. 

them parallel, after which both screws must be tightened. Test the 
adjustment by again measuring a ic/ space with the micrometer. If 
it is still out of adjustment, repeat these operations till it is satisfac- 
tory. When the adjustment has been completed, a scratch may be 
made on the tube below each support and used as a guide in future 
adjustments. 

The opposite micrometers may be placed 180 apart by setting one 
at a reading of o° o / o 7/ , with the comb scale exactly centered. Then 
center the comb scale of the other micrometer over the 180 mark by 
means of the capstan-headed screw at the left-hand end of its box. 
Bring the micrometer threads over the 180 mark also; then, while 
holding the screw firmly in place, turn the graduated ring till it reads 
zero. 

When setting the micrometer wires on a graduation, it is very 
important that they be moving toward the right when the turning of 
the screw is stopped. Should they be moved the least bit too far to 
the right, turn back not less than half a revolution of the screw and 
then bring them forward again. In general, when a setting is made 
by means of a screw working against a spring, the spring should 
always be undergoing compression when the motion stops. 

Cross wires. — The vertical wire should be truly vertical; otherwise 
an exact adjustment of the cross wires is not essential. 

After the striding level has been adjusted and the horizontal axis 
of the telescope carefully leveled, sight a distant point, raise and 
lower the telescope through an angle of 5 or io°, and note whether 
the cross wires follow the point. If not, loosen the cross- wire ring 
and twist slightly;, repeat the adjustment if necessary. 

Hold the striding level on the telescope parallel to the optical axis 
and, with the bubble in the center of the tube, set the intersection 
of the cross wires on a distant point and clamp both plates; lift the 
telescope out of its supports and turn 180 around its optical axis; 
set it again on the selected point. If the striding level when placed 
on top of the telescope is horizontal, the adjustment is complete. If 
not, shift the cross wires in either direction by means of the capstan- 
headed screws for one-half the apparent error. Repeat the test till 
the error is nearly all eliminated. Finally readjust the vertical wire, 
if necessary. 

LBJL '12 ° 



